02:27Simplify Square Roots of Perfect Squares: Square Root of 81 & (121/144), Negative Square Root of 64Wendy692views
Textbook QuestionIn this Exercise Set, assume that all variables represent positive real numbers. In Exercises 1–10, add or subtract as indicated. _ _ 7√3 + 2√3174views
Textbook QuestionDetermine whether each statement is true or false. If false, correct the right side of the equation. (y^2)(y^5) = y^7251views
Textbook QuestionMatch the rational exponent expression in Column I with the equivalent radical expression in Column II. Assume that x is not 0. (c) ( 3x )^1/3341views
Textbook QuestionMatch the rational exponent expression in Column I with the equivalent radical expression in Column II. Assume that x is not 0. (d) ( 3x )^-1/3398views
Textbook QuestionMatch the rational exponent expression in Column I with the equivalent radical expression in Column II. Assume that x is not 0. (b) ( -3x )^-1/3245views
Textbook QuestionMatch the rational exponent expression in Column I with the equivalent radical expression in Column II. Assume that x is not 0. (a) ( -3x )^1/3301views
Textbook QuestionIn Exercises 1–20, use radical notation to rewrite each expression. Simplify, if possible. (-27)^⅓161views
Textbook QuestionIn Exercises 1–20, evaluate each expression, or state that the expression is not a real number. ___ -√ 36179views
Textbook QuestionMatch the rational exponent expression in Column I with the equivalent radical expression in Column II. Assume that x is not 0. (a) -3x^1/3321views
Textbook QuestionMatch the rational exponent expression in Column I with the equivalent radical expression in Column II. Assume that x is not 0. (d) 3x^1/3212views
Textbook QuestionMatch the rational exponent expression in Column I with the equivalent radical expression in Column II. Assume that x is not 0. (c) 3x^-1/3240views
Textbook QuestionIn Exercises 4–6, evaluate each algebraic expression for the given value or values of the variable. 6+2(x-8)³, for x=11176views
Textbook QuestionIn Exercises 1–20, use radical notation to rewrite each expression. Simplify, if possible. -16^¼178views
Textbook QuestionIn Exercises 1–20, evaluate each expression, or state that the expression is not a real number. ___ √-36176views
Textbook QuestionEvaluate each expression in Exercises 1–12, or indicate that the root is not a real number. √−25347views
Textbook QuestionIn Exercises 1–38, multiply as indicated. If possible, simplify any radical expressions that appear in the product. √6 (4√6 - 3√2)161views
Textbook QuestionIn Exercises 1–20, use radical notation to rewrite each expression. Simplify, if possible. (xy)^⅓158views
Textbook QuestionIn Exercises 1–20, evaluate each expression, or state that the expression is not a real number. ____ √1/25179views
Textbook QuestionPerform the operation and/or simplify each of the following. Assume all variables represent positive real numbers. √50254views
Textbook QuestionEvaluate each expression in Exercises 1–12, or indicate that the root is not a real number. √144+25286views
Textbook QuestionDetermine whether each statement is true or false. If false, correct the right side of the equation. (m^2/3)(m^1/3) = m^2/9274views
Textbook QuestionIn Exercises 1–38, multiply as indicated. If possible, simplify any radical expressions that appear in the product. ³√3 (³√6 + 7 ³√4)171views
Textbook QuestionIn Exercises 1–20, use radical notation to rewrite each expression. Simplify, if possible. (2xy³)^⅕248views
Textbook QuestionIn Exercises 1–20, evaluate each expression, or state that the expression is not a real number. ____ -√9/16171views
Textbook QuestionPerform the operation and/or simplify each of the following. Assume all variables represent positive real numbers. 3√xy - 8√xy217views
Textbook QuestionEvaluate each expression in Exercises 1–12, or indicate that the root is not a real number. √25−√16246views
Textbook QuestionPerform the operation and/or simplify each of the following. Assume all variables represent positive real numbers. (2 + √3) (2 - √3)241views
Textbook QuestionMatch each expression in Column I with its equivalent expression in Column II. Choices may be used once, more than once, or not at all. a. 5^-3 b. -5^-3 c. (-5)^-3 d. -(-5)^-3 A. 125 B. -125 C. 1/125 D. -1/125342views
Textbook QuestionIn Exercises 1–38, multiply as indicated. If possible, simplify any radical expressions that appear in the product. ³√x (³√24x² - ³√x)166views
Textbook QuestionIn this Exercise Set, assume that all variables represent positive real numbers. In Exercises 1–10, add or subtract as indicated. _ _ _ _ 6√7 - ³√x + 2√7 + 5³√x200views
Textbook QuestionIn Exercises 1–20, use radical notation to rewrite each expression. Simplify, if possible. 81^3/2162views
Textbook QuestionIn Exercises 1–20, evaluate each expression, or state that the expression is not a real number. ____ √0.81184views
Textbook QuestionEvaluate each expression in Exercises 1–12, or indicate that the root is not a real number. √(−17)^2267views
Textbook QuestionIn Exercises 1–38, multiply as indicated. If possible, simplify any radical expressions that appear in the product. (7 + √2) (8 + √2)163views
Textbook QuestionIn Exercises 11–28, add or subtract as indicated. You will need to simplify terms to identify the like radicals. _ __ √5 + √20158views
Textbook QuestionIn Exercises 1–20, use the product rule to multiply. ___ _____ ⁶√x-5 ⋅ ⁶√(x-5)⁴179views
Textbook QuestionIn Exercises 1–38, multiply as indicated. If possible, simplify any radical expressions that appear in the product. (4 + √5) (10 - 3√5)170views
Textbook QuestionIn Exercises 11–28, add or subtract as indicated. You will need to simplify terms to identify the like radicals. __ __ 5√12 + √75147views
Textbook QuestionIn Exercises 1–38, solve each radical equation. _____ _____ √6x + 2 = √5x + 3164views
Textbook QuestionIn Exercises 1–38, multiply as indicated. If possible, simplify any radical expressions that appear in the product. (7 - 2√7) (5 - 3√7)169views
Textbook QuestionIn Exercises 11–28, add or subtract as indicated. You will need to simplify terms to identify the like radicals. ___ ___ 5√45x - 2√20x161views
Textbook QuestionUse the product rule to simplify the expressions in Exercises 13–22. In Exercises 17–22, assume that variables represent nonnegative real numbers. √10x⋅√ 8x304views
Textbook QuestionIn Exercises 11–28, add or subtract as indicated. You will need to simplify terms to identify the like radicals. __ __ 3³√24 + ³√81167views
Textbook QuestionIn Exercises 1–20, use radical notation to rewrite each expression. Simplify, if possible. (xy)^4/7231views
Textbook QuestionIn Exercises 1–20, evaluate each expression, or state that the expression is not a real number. ______ √16 − 25187views
Textbook QuestionUse the product rule to simplify the expressions in Exercises 13–22. In Exercises 17–22, assume that variables represent nonnegative real numbers. √6x⋅√3x^2656views
Textbook QuestionIn Exercises 1–38, solve each radical equation. ____ ____ √x - 4 + √x + 4 = 4185views
Textbook QuestionIn Exercises 1–38, multiply as indicated. If possible, simplify any radical expressions that appear in the product. (√2 + √7)²165views
Textbook QuestionSimplify each expression. Assume all variables represent nonzero real numbers. See Examples 1–3. (6^4)^3246views
Textbook QuestionIn Exercises 25–34, use the zero-exponent rule to simplify each expression. 6⁰180views
Textbook QuestionIn Exercises 21–38, rewrite each expression with rational exponents. ___ ⁵√11x311views
Textbook QuestionIn Exercises 1–38, multiply as indicated. If possible, simplify any radical expressions that appear in the product. (√2x - √y)²163views
Textbook QuestionSimplify each expression. Assume all variables represent nonzero real numbers. See Examples 1–3. (-2x^5)^5249views
Textbook QuestionIn Exercises 11–28, add or subtract as indicated. You will need to simplify terms to identify the like radicals. ______ ___ √4x - 12 + √x-3144views
Textbook QuestionIf the expression is in exponential form, write it in radical form and evaluate if possible. If it is in radical form, write it in exponential form. Assume all variables represent posi-tive real numbers. -5z^2/3649views
Textbook QuestionIn Exercises 1–38, multiply as indicated. If possible, simplify any radical expressions that appear in the product. (√6 + √2) (√6 - √2)164views
Textbook QuestionSimplify each expression. Assume all variables represent nonzero real numbers. See Examples 1–3. -(2x^0y^4)^3241views
Textbook QuestionIn Exercises 11–28, add or subtract as indicated. You will need to simplify terms to identify the like radicals. ___ ___ 4³√x⁴y² + 5x³√xy²166views
Textbook QuestionIf the expression is in exponential form, write it in radical form and evaluate if possible. If it is in radical form, write it in exponential form. Assume all variables represent posi-tive real numbers. p^5/4389views
Textbook QuestionIn Exercises 1–38, multiply as indicated. If possible, simplify any radical expressions that appear in the product. (3 - 5√2) (3 + 5√2)158views
Textbook QuestionSimplify each expression. Assume all variables represent nonzero real numbers. See Examples 1–3. (p^4/q)^2344views
Textbook QuestionIf the expression is in exponential form, write it in radical form and evaluate if possible. If it is in radical form, write it in exponential form. Assume all variables represent posi-tive real numbers. (5r + 3t)^4/7442views
Textbook QuestionUse the quotient rule to simplify the expressions in Exercises 23–32. Assume that x > 0. √24x^4/√3x590views
Textbook QuestionIf the expression is in exponential form, write it in radical form and evaluate if possible. If it is in radical form, write it in exponential form. Assume all variables represent posi-tive real numbers. ⁵√ k²325views
Textbook QuestionIn Exercises 1–38, multiply as indicated. If possible, simplify any radical expressions that appear in the product. (4√3 + 3√2) (4√3 - 3√2)160views
Textbook QuestionSimplify each expression. Assume all variables represent nonzero real numbers. See Examples 1–3. (-5n^4/r^2)^3721views
Textbook QuestionUse the quotient rule to simplify the expressions in Exercises 23–32. Assume that x > 0. √500x^3/√10x^−1283views
Textbook QuestionSimplify each expression. Assume all variables represent nonzero real numbers. See Examples 1–3. -(x^3y^5/z)^0693views
Textbook QuestionIf the expression is in exponential form, write it in radical form and evaluate if possible. If it is in radical form, write it in exponential form. Assume all variables represent posi-tive real numbers. -3 √5p³395views
Textbook QuestionIn Exercises 25–34, use the zero-exponent rule to simplify each expression. (13y)⁰274views
Textbook QuestionIf the expression is in exponential form, write it in radical form and evaluate if possible. If it is in radical form, write it in exponential form. Assume all variables represent posi-tive real numbers. -m √2y⁵232views
Textbook QuestionIn Exercises 1–38, solve each radical equation. ____ _____ √x + 2 + √3x + 7 = 1244views
Textbook QuestionIn Exercises 33–38, express the function, f, in simplified form. Assume that x can be any real number. _______ f(x) = √81(x-2)²161views
Textbook QuestionMatch each expression in Column I with its equivalent expression in Column II. Choices may be used once, more than once, or not at all. See Example 3. a. 6^0 b. -6^0 c. (-6)^0 d. -(-6)^0 A. 0 B. 1 C. -1 D. 6 E. -6323views
Textbook QuestionIn Exercises 35–52, write each expression with positive exponents only. Then simplify, if possible. 3⁻²164views
Textbook QuestionIn Exercises 21–38, rewrite each expression with rational exponents. ____ (⁶√7xy² ) ⁵170views
Textbook QuestionIn Exercises 33–38, express the function, f, in simplified form. Assume that x can be any real number. _______ f(x) = ³√48(x-2)³174views
Textbook QuestionIn Exercises 35–52, write each expression with positive exponents only. Then simplify, if possible. (-5)⁻²164views
Textbook QuestionIn Exercises 21–38, rewrite each expression with rational exponents. __ 2x ³√y²171views
Textbook QuestionIn Exercises 33–38, express the function, f, in simplified form. Assume that x can be any real number. ___________ f(x) = √5x² - 10x + 5198views
Textbook QuestionIn Exercises 35–52, write each expression with positive exponents only. Then simplify, if possible. -5⁻²308views
Textbook QuestionIn Exercises 39–54, rewrite each expression with a positive rational exponent. Simplify, if possible. 49^-½176views
Textbook QuestionWrite each expression without negative exponents, and evaluate if possible. Assume all variables represent nonzero real numbers. See Example 4. -5^-4291views
Textbook QuestionIn Exercises 39–60, simplify by factoring. Assume that all variables in a radicand represent positive real numbers and no radicands involve negative quantities raised to even powers. __ √x⁵168views
Textbook QuestionIn Exercises 35–52, write each expression with positive exponents only. Then simplify, if possible. x²y⁻³163views
Textbook QuestionIn Exercises 39–54, rewrite each expression with a positive rational exponent. Simplify, if possible. 27^-⅓156views
Textbook QuestionWrite each expression without negative exponents, and evaluate if possible. Assume all variables represent nonzero real numbers. See Example 4. (1/3)^-2239views
Textbook QuestionIn Exercises 39–60, simplify by factoring. Assume that all variables in a radicand represent positive real numbers and no radicands involve negative quantities raised to even powers. ___ √x⁶y⁷154views
Textbook QuestionIn Exercises 39–54, rewrite each expression with a positive rational exponent. Simplify, if possible. 16^-¾178views
Textbook QuestionIn Exercises 33–44, add or subtract terms whenever possible. 3√8−√32+3√72−√75316views
Textbook QuestionWrite each expression without negative exponents, and evaluate if possible. Assume all variables represent nonzero real numbers. See Example 4. (4x)^-2510views
Textbook QuestionWrite each expression without negative exponents, and evaluate if possible. Assume all variables represent nonzero real numbers. See Example 4. 4x^-2256views
Textbook QuestionUse the rules for radicals to perform the indicated operations. Assume all variable expressions represent positive real numbers. √7 • √28236views
Textbook QuestionWrite each expression without negative exponents, and evaluate if possible. Assume all variables represent nonzero real numbers. See Example 4. -a^-3257views
Textbook QuestionIn Exercises 39–60, simplify by factoring. Assume that all variables in a radicand represent positive real numbers and no radicands involve negative quantities raised to even powers. _____ ³√x³y¹⁷z²192views
Textbook QuestionIn Exercises 35–52, write each expression with positive exponents only. Then simplify, if possible. x⁻²/y⁻⁵168views
Textbook QuestionIn Exercises 39–60, simplify by factoring. Assume that all variables in a radicand represent positive real numbers and no radicands involve negative quantities raised to even powers. ______ ³√32x⁹y¹⁷171views
Textbook QuestionIn Exercises 35–52, write each expression with positive exponents only. Then simplify, if possible. a⁻⁴b⁷/c⁻³194views
Textbook QuestionIn Exercises 39–54, rewrite each expression with a positive rational exponent. Simplify, if possible. (2xy)^-7/10201views
Textbook QuestionUse the rules for radicals to perform the indicated operations. Assume all variable expressions represent positive real numbers. ⁵√x² • ⁵√x³310views
Textbook QuestionIn Exercises 39–60, simplify by factoring. Assume that all variables in a radicand represent positive real numbers and no radicands involve negative quantities raised to even powers. _____ ³√(x+y)⁴156views
Textbook QuestionIn Exercises 39–54, rewrite each expression with a positive rational exponent. Simplify, if possible. 5xz^-⅓170views
Textbook QuestionUse the rules for radicals to perform the indicated operations. Assume all variable expressions represent positive real numbers. ∜ m² • ∜ m²246views
Textbook QuestionIn Exercises 39–60, simplify by factoring. Assume that all variables in a radicand represent positive real numbers and no radicands involve negative quantities raised to even powers. ___ ⁵√y¹⁸206views
Textbook QuestionSimplify each expression. Write answers without negative exponents. Assume all vari-ables represent nonzero real numbers. See Examples 5 and 6. y^8/y^12243views
Textbook QuestionIn Exercises 55–58, find the indicated function values for each function. ___ f(x) = ³√x−1; f(28), f(9), f(0), f(−63)205views
Textbook QuestionSimplify each expression. Write answers without negative exponents. Assume all vari-ables represent nonzero real numbers. See Examples 5 and 6. 6^4/6^-2223views
Textbook QuestionIn Exercises 55–78, use properties of rational exponents to simplify each expression. Assume that all variables represent positive numbers. 3^¾ ⋅ 3^¼172views
Textbook QuestionUse the rules for radicals to perform the indicated operations. Assume all variable expressions represent positive real numbers. √14 • √3pqr368views
Textbook QuestionEvaluate each expression in Exercises 55–66, or indicate that the root is not a real number. ³√8280views
Textbook QuestionIn Exercises 45–66, divide and, if possible, simplify. ______ √54a⁷b¹¹ √3a⁻⁴b⁻²160views
Textbook QuestionIn Exercises 55–58, find the indicated function values for each function. ____ g(x) = −³√8x−8; g(2), g(1), g(0)172views
Textbook QuestionSimplify each expression. Write answers without negative exponents. Assume all vari-ables represent nonzero real numbers. See Examples 5 and 6. 4r^-3/6r^-6247views
Textbook QuestionIn Exercises 55–78, use properties of rational exponents to simplify each expression. Assume that all variables represent positive numbers. 16^¾ 16^¼160views
Textbook QuestionUse the rules for radicals to perform the indicated operations. Assume all variable expressions represent positive real numbers. ∛ 7x • ∛ 2y240views
Textbook QuestionSimplify each exponential expression in Exercises 23–64. 10x^4 y^9/30x^12 y^−3281views
Textbook QuestionIn Exercises 59–72, simplify each expression using the products-to-powers rule. (4x)³154views
Textbook QuestionUse the rules for radicals to perform the indicated operations. Assume all variable expressions represent positive real numbers. √9/25282views
Textbook QuestionSimplify each expression. Write answers without negative exponents. Assume all vari-ables represent nonzero real numbers. See Examples 5 and 6. 16m^-5n^4/12m^2n^-3430views
Textbook QuestionIn Exercises 55–78, use properties of rational exponents to simplify each expression. Assume that all variables represent positive numbers. x^½ ⋅ x^⅓157views
Textbook QuestionEvaluate each expression in Exercises 55–66, or indicate that the root is not a real number. ⁴√−16269views
Textbook QuestionIn Exercises 45–66, divide and, if possible, simplify. ______ ³√250x⁵y³ ³√2x³178views
Textbook QuestionIn Exercises 55–78, use properties of rational exponents to simplify each expression. Assume that all variables represent positive numbers. x^⅘ x^⅕165views
Textbook QuestionUse the rules for radicals to perform the indicated operations. Assume all variable expressions represent positive real numbers. - ∛5/8213views
Textbook QuestionSimplify each expression. Write answers without negative exponents. Assume all vari-ables represent nonzero real numbers. See Examples 5 and 6. -4r^-2(r^4)^2271views
Textbook QuestionIn Exercises 45–66, divide and, if possible, simplify. ______ ⁵√96x¹²y¹¹ ⁵√3x²y⁻²162views
Textbook QuestionSimplify the radical expressions in Exercises 58 - 62. ∜(32x^5)/∜(16x) (Assume that x > 0.)321views
Textbook QuestionUse the rules for radicals to perform the indicated operations. Assume all variable expressions represent positive real numbers. ∜m/n⁴333views
Textbook QuestionEvaluate each expression in Exercises 55–66, or indicate that the root is not a real number. ⁵√(−3)^5309views
Textbook QuestionSimplify each exponential expression in Exercises 23–64. (3a^−5 b^2/12a^3 b^−4)^0299views
Textbook QuestionSimplify each expression. Write answers without negative exponents. Assume all vari-ables represent nonzero real numbers. See Examples 5 and 6. (5a^-1)^4(a^2)^-3241views
Textbook QuestionIn Exercises 45–66, divide and, if possible, simplify. _______ ³√x²+7x+12 ³√x+3148views
Textbook QuestionIn Exercises 61–82, multiply and simplify. Assume that all variables in a radicand represent positive real numbers and no radicands involve negative quantities raised to even powers. __ ___ √8x ⋅ √10y165views
Textbook QuestionSimplify each expression. Write answers without negative exponents. Assume all vari-ables represent nonzero real numbers. See Examples 5 and 6. (p^-2)^0/5p^-4218views
Textbook QuestionIn Exercises 59–76, find the indicated root, or state that the expression is not a real number. ___ ⁴√−16162views
Textbook QuestionEvaluate each expression in Exercises 55–66, or indicate that the root is not a real number. ⁶√1/64340views
Textbook QuestionIn Exercises 65–74, simplify each radical expression and then rationalize the denominator. 25 --------- √5x²y157views
Textbook QuestionSimplify each expression. Write answers without negative exponents. Assume all vari-ables represent nonzero real numbers. See Examples 5 and 6. (3pq)q^2/6p^2q^4480views
Textbook QuestionIn Exercises 59–76, find the indicated root, or state that the expression is not a real number. ___ ⁵√−1184views
Textbook QuestionIn Exercises 59–72, simplify each expression using the products-to-powers rule. (-3x⁻²)⁻³154views
Textbook QuestionUse the rules for radicals to perform the indicated operations. Assume all variable expressions represent positive real numbers. ∜∛2288views
Textbook QuestionIn Exercises 65–74, simplify each radical expression and then rationalize the denominator. 150a³ - √ ---------- b⁵165views
Textbook QuestionIn Exercises 61–82, multiply and simplify. Assume that all variables in a radicand represent positive real numbers and no radicands involve negative quantities raised to even powers. ___ _____ √5xy ⋅ √10xy²150views
Textbook QuestionUse the rules for radicals to perform the indicated operations. Assume all variable expressions represent positive real numbers. ⁵√∛9274views
Textbook QuestionSimplify each expression. Write answers without negative exponents. Assume all vari-ables represent nonzero real numbers. See Examples 5 and 6. 4a^5(a^-1)^3/(a^-2)^-2471views
Textbook QuestionIn Exercises 59–76, find the indicated root, or state that the expression is not a real number. ___ ⁶√−1161views
Textbook QuestionIn Exercises 59–72, simplify each expression using the products-to-powers rule. (5x³y⁻⁴)⁻²162views
Textbook QuestionIn Exercises 55–78, use properties of rational exponents to simplify each expression. Assume that all variables represent positive numbers. (2x^⅕)⁵151views
Textbook QuestionIn Exercises 65–74, simplify each radical expression and then rationalize the denominator. 5m⁴n⁶ √ ------------- 15m³n⁴162views
Textbook QuestionIn Exercises 61–82, multiply and simplify. Assume that all variables in a radicand represent positive real numbers and no radicands involve negative quantities raised to even powers. __ _ 3√15 ⋅ 5√6166views
Textbook QuestionIn Exercises 59–76, find the indicated root, or state that the expression is not a real number. ___ −⁴√256156views
Textbook QuestionIn Exercises 59–72, simplify each expression using the products-to-powers rule. (-2x⁻⁵y⁴z²)⁻⁴158views
Textbook QuestionIn Exercises 55–78, use properties of rational exponents to simplify each expression. Assume that all variables represent positive numbers. (25x⁴y⁶)^½256views
Textbook QuestionSimplify each radical. Assume all variables represent positive real numbers. √192469views
Textbook QuestionIn Exercises 59–76, find the indicated root, or state that the expression is not a real number. __ ⁶√64177views
Textbook QuestionIn Exercises 55–78, use properties of rational exponents to simplify each expression. Assume that all variables represent positive numbers. (x^½y^-⅗)^½164views
Textbook QuestionIn Exercises 73–84, simplify each expression using the quotients-to-powers rule. (2/x)⁴148views
Textbook QuestionSimplify the radical expressions in Exercises 67–74, if possible. ⁵√64x^6/⁵√2x484views
Textbook QuestionIn Exercises 65–74, simplify each radical expression and then rationalize the denominator. 15 ------------ ³√-27x⁴y¹¹158views
Textbook QuestionSimplify each radical. Assume all variables represent positive real numbers. ∛250272views
Textbook QuestionIn Exercises 55–78, use properties of rational exponents to simplify each expression. Assume that all variables represent positive numbers. 3^½ ⋅ 3^¾ 3^¼160views
Textbook QuestionIn Exercises 73–84, simplify each expression using the quotients-to-powers rule. (x³/5)²195views
Textbook QuestionSimplify each radical. Assume all variables represent positive real numbers. - ∜2431014views
Textbook QuestionIn Exercises 75–92, rationalize each denominator. Simplify, if possible. 15 ---------- √6 + 1170views
Textbook QuestionIn Exercises 55–78, use properties of rational exponents to simplify each expression. Assume that all variables represent positive numbers. (3y^¼)³ y^1/12293views
Textbook QuestionIn Exercises 73–84, simplify each expression using the quotients-to-powers rule. (- 3x/y)⁴160views
Textbook QuestionIn Exercises 77–90, simplify each expression. Include absolute value bars where necessary. __ ³√x³163views
Textbook QuestionSimplify each radical. Assume all variables represent positive real numbers. -9 ⁵√243277views
Textbook QuestionIn Exercises 75–92, rationalize each denominator. Simplify, if possible. 17 ---------- √10 - 2153views
Textbook QuestionIn Exercises 79–112, use rational exponents to simplify each expression. If rational exponents appear after simplifying, write the answer in radical notation. Assume that all variables represent positive numbers. __ ⁸√x²168views
Textbook QuestionIn Exercises 77–90, simplify each expression. Include absolute value bars where necessary. __ ⁴√y⁴172views
Textbook QuestionIn Exercises 75–82, add or subtract terms whenever possible. ³√54xy^3−y³√128x273views
Textbook QuestionIn Exercises 75–92, rationalize each denominator. Simplify, if possible. 12 ------------ √7 + √3151views
Textbook QuestionSimplify each radical. Assume all variables represent positive real numbers. ∛(16 (-2)⁴ (2)⁸)307views
Textbook QuestionMatch each expression in Column I with its equivalent expression in Column II. See Example 8. a. (4/9)^3/2 b. (4/9)^-3/2 c. -(9/4)^3/2 d. -(9/4)^-3/2 A. 27/8 B. -27/8 C. 8/27 D. -8/27257views
Textbook QuestionIn Exercises 79–112, use rational exponents to simplify each expression. If rational exponents appear after simplifying, write the answer in radical notation. Assume that all variables represent positive numbers. ___ ³√8a⁶174views
Textbook QuestionIn Exercises 77–90, simplify each expression. Include absolute value bars where necessary. ____ ³√−8x³162views
Textbook QuestionIn Exercises 75–92, rationalize each denominator. Simplify, if possible. √b ---------- √a - √b146views
Textbook QuestionSimplify each expression. Write answers without negative exponents. Assume all vari-ables represent positive real numbers. See Examples 8 and 9. 8^2/3436views
Textbook QuestionIn Exercises 79–112, use rational exponents to simplify each expression. If rational exponents appear after simplifying, write the answer in radical notation. Assume that all variables represent positive numbers. _____ ⁵√x¹⁰y¹⁵157views
Textbook QuestionIn Exercises 77–90, simplify each expression. Include absolute value bars where necessary. ____ ³√(−5)³165views
Textbook QuestionSimplify each radical. Assume all variables represent positive real numbers. √24m⁶n⁵271views
Textbook QuestionSimplify each radical. Assume all variables represent positive real numbers. ∜(x⁴ + y⁴)286views
Textbook QuestionSimplify each radical. Assume all variables represent positive real numbers. ∛(27 + a³)237views
Textbook QuestionSimplify each radical. Assume all variables represent positive real numbers. ⁹√5³264views
Textbook QuestionSimplify each radical. Assume all variables represent positive real numbers. ⁶√11³244views
Textbook QuestionIn Exercises 83–90, evaluate each expression without using a calculator. 16^(−6/2)306views
Textbook QuestionSimplify each radical. Assume all variables represent positive real numbers. ⁸√5⁴296views
Textbook QuestionIn Exercises 75–92, rationalize each denominator. Simplify, if possible. 2√6 + √5 -------------- 3√6 - √5145views
Textbook QuestionSimplify each radical. Assume all variables represent positive real numbers. ⁶√x¹⁸y²697views
Textbook QuestionSimplify each expression. Write answers without negative exponents. Assume all vari-ables represent positive real numbers. See Examples 8 and 9. (3^1/2)(3^3/2)456views
Textbook QuestionIn Exercises 79–112, use rational exponents to simplify each expression. If rational exponents appear after simplifying, write the answer in radical notation. Assume that all variables represent positive numbers. ____ ⁹√x⁶y³162views
Textbook QuestionSimplify each expression. Write answers without negative exponents. Assume all vari-ables represent positive real numbers. See Examples 8 and 9. (64^5/3)/(64^4/3)278views
Textbook QuestionIn Exercises 93–104, rationalize each numerator. Simplify, if possible. 5 √ --- 3184views
Textbook QuestionSimplify each radical. Assume all variables represent positive real numbers. ⁹√∜7³250views
Textbook QuestionSimplify each expression. Write answers without negative exponents. Assume all vari-ables represent positive real numbers. See Examples 8 and 9. (y^7/3)(y^-4/3)252views
Textbook QuestionPerform the indicated operations. Assume all variables represent positive real numbers. 8√(2x) - √(8x) + √(72x)700views
Textbook QuestionIn Exercises 93–104, rationalize each numerator. Simplify, if possible. ³√2x ³√y160views
Textbook QuestionSimplify each expression. Write answers without negative exponents. Assume all vari-ables represent positive real numbers. See Examples 8 and 9. (k^1/3)/(k^2/3)(k^-1)306views
Textbook QuestionPerform the indicated operations. Assume all variables represent positive real numbers. 3√72m² - 5√32m² - 3√18m²235views
Textbook QuestionIn Exercises 79–112, use rational exponents to simplify each expression. If rational exponents appear after simplifying, write the answer in radical notation. Assume that all variables represent positive numbers. ___ __ ⁴√a²b ⋅ ³√ab161views
Textbook QuestionIn Exercises 85–116, simplify each exponential expression. (-¼x⁻⁴y⁵z⁻¹)(-12x⁻³y⁻¹z⁴)162views
Textbook QuestionSimplify each expression. Write answers without negative exponents. Assume all vari-ables represent positive real numbers. See Examples 8 and 9. (z^3/4)/(z^5/4)(z^-2)307views
Textbook QuestionIn Exercises 93–104, rationalize each numerator. Simplify, if possible. √x + 4 √x167views
Textbook QuestionSimplify each expression. Write answers without negative exponents. Assume all vari-ables represent positive real numbers. See Examples 8 and 9. (x^1/4y^2/5)^20/x^2393views
Textbook QuestionPerform the indicated operations. Assume all variables represent positive real numbers. 2∛3 + 4∛24 - ∛81244views
Textbook QuestionIn Exercises 79–112, use rational exponents to simplify each expression. If rational exponents appear after simplifying, write the answer in radical notation. Assume that all variables represent positive numbers. _ ⁴√x ⁵√x181views
Textbook QuestionIn Exercises 93–104, rationalize each numerator. Simplify, if possible. √a - √b √a + √b227views
Textbook QuestionPerform the indicated operations. Assume all variables represent positive real numbers. ∜32 + 3∜2237views
Textbook QuestionIn Exercises 79–112, use rational exponents to simplify each expression. If rational exponents appear after simplifying, write the answer in radical notation. Assume that all variables represent positive numbers. __ ³√y² ⁶√y167views
Textbook QuestionPerform the indicated operations. Assume all variables represent positive real numbers. 2∛16 + ∛54229views
Textbook QuestionIn Exercises 79–112, use rational exponents to simplify each expression. If rational exponents appear after simplifying, write the answer in radical notation. Assume that all variables represent positive numbers. __ ⁴√√x159views
Textbook QuestionIn Exercises 103–110, insert either <, >, or = in the shaded area to make a true statement. |−20| □ |−50|280views
Textbook QuestionPerform the indicated operations. Assume all variables represent positive real numbers. 3x∛xy² - 2∛8x⁴y²247views
Textbook QuestionIn Exercises 79–112, use rational exponents to simplify each expression. If rational exponents appear after simplifying, write the answer in radical notation. Assume that all variables represent positive numbers. ____ √√x²y161views
Textbook QuestionIn Exercises 85–116, simplify each exponential expression. -24a³b⁻⁵c⁵/-3a⁻⁶b⁻⁴c⁻⁷166views
Textbook QuestionIn Exercises 105–110, use an associative property to write an algebraic expression equivalent to each expression and simplify. 4+(6+x)159views
Textbook QuestionSimplify each expression. Write answers without negative exponents. Assume all vari-ables represent positive real numbers. See Examples 8 and 9. (z^1/3z^-2/3z^1/6)/(z^-1/6)^3343views
Textbook QuestionIn Exercises 103–110, insert either <, >, or = in the shaded area to make a true statement. 30/40−3/4 □ 14/15⋅15/14308views
Textbook QuestionIn Exercises 107–114, simplify each exponential expression. Assume that variables represent nonzero real numbers. (x^−2 y)^−3/(x^2 y^−1)^3343views
Textbook QuestionIn Exercises 101–108, simplify by reducing the index of the radical. ⁹√x^6 y^3308views
Textbook QuestionIn Exercises 101–108, simplify by reducing the index of the radical. ¹²√x^4y^8300views
Textbook QuestionPerform the indicated operations. Assume all variables represent positive real numbers. ∛64xy² + ∛27x⁴y⁵245views
Textbook QuestionIn Exercises 107–114, simplify each exponential expression. Assume that variables represent nonzero real numbers. (3x−4 y z−7)(3x)−3280views
Textbook QuestionIn Exercises 111–114, simplify each expression. Assume that all variables represent positive numbers. (49x^−2y^4)^−1/2(xy^1/2)340views
Textbook QuestionPerform the indicated operations. Assume all variables represent positive real numbers. ∜81x⁶y³ - ∜16x¹⁰y³250views
Textbook QuestionIn Exercises 111–114, simplify each expression. Assume that all variables represent positive numbers. (x^−5/4y^1/3x^−3/4)^−6612views
Textbook QuestionPerform the indicated operations. Assume all variables represent positive real numbers. 5√6 + 2√10302views
Textbook QuestionIn Exercises 107–114, simplify each exponential expression. Assume that variables represent nonzero real numbers. (2^−1x^−3y^−1)^−2(2x^−6y^4)^−2(9x^3y^−3)^0/(2x^−4y^−6)^2271views
Textbook QuestionPerform the indicated operations. Assume all variables represent positive real numbers. √6(3 + √7)277views
Textbook QuestionIn Exercises 85–116, simplify each exponential expression. (20a⁻³b⁴c⁵/-2a⁻⁵b⁻²c)⁻²155views
Textbook QuestionPerform the indicated operations. Assume all variables represent positive real numbers. 4√3(√7 - 2√11)264views
Textbook QuestionIn Exercises 117–124, simplify each exponential expression. 9y⁴/x⁻² + (x⁻¹/y²)⁻²171views
Textbook QuestionPerform the indicated operations. Assume all variables represent positive real numbers. (√2 + 3) (√2 - 3)220views
Textbook QuestionMake Sense? In Exercises 119–122, determine whether each statement makes sense or does not make sense, and explain your reasoning. ____ ⁴√(−8)⁴ cannot be positive 8 because the power and the index cancel each other.168views
Textbook QuestionIn Exercises 117–124, simplify each exponential expression. (3x⁴/y⁻⁴)⁻¹(2x/y²)³178views
Textbook QuestionPerform the indicated operations. Assume all variables represent positive real numbers. (∛11 - 1) (∛11² + ∛11 +1)258views
Textbook QuestionIn Exercises 117–124, simplify each exponential expression. (-4x³y⁻⁵)⁻²(2x⁻⁸y⁻⁵)172views
Textbook QuestionIn Exercises 117–124, simplify each exponential expression. (2x²y⁴)⁻¹(4xy³)⁻³ / (x²y)⁻⁵(x³y²)⁴226views
Textbook QuestionPerform the indicated operations. Assume all variables represent positive real numbers. (3√2 + √3) (2√3 - √2)234views
Textbook QuestionPerform the indicated operations and/or simplify each expression. Assume all variables represent positive real numbers. 5/√2229views
Textbook QuestionPerform the indicated operations and/or simplify each expression. Assume all variables represent positive real numbers. ∛2/3286views
Textbook QuestionPerform the indicated operations and/or simplify each expression. Assume all variables represent positive real numbers. ∜2/25243views
Textbook QuestionPerform the indicated operations and/or simplify each expression. Assume all variables represent positive real numbers. √2/3x279views
Textbook QuestionPerform the indicated operations and/or simplify each expression. Assume all variables represent positive real numbers. √(x⁵y³)/z²306views
Textbook QuestionPerform the indicated operations and/or simplify each expression. Assume all variables represent positive real numbers. ∛8/x⁴247views
Textbook QuestionPerform the indicated operations and/or simplify each expression. Assume all variables represent positive real numbers. (∛mn • ∛m²) / ∛n²229views
Textbook QuestionPerform the indicated operations and/or simplify each expression. Assume all variables represent positive real numbers. (-4 /∛3 ) + (1/∛24) - ( 2/∛81)232views
Textbook QuestionPerform the indicated operations and/or simplify each expression. Assume all variables represent positive real numbers. ( 5/∛2) - ( 2/∛16) + (1/∛54)292views
Textbook QuestionRationalize each denominator. Assume all variables represent nonnegative numbers and that no denominators are 0. 1/(2 + √5)294views
Textbook QuestionRationalize each denominator. Assume all variables represent nonnegative numbers and that no denominators are 0. (√7 - 1) / (2√7 + 4√2)346views
Textbook QuestionRationalize each denominator. Assume all variables represent nonnegative numbers and that no denominators are 0. (p - 4) / (√p + 2)355views
Textbook QuestionRationalize each denominator. Assume all variables represent nonnegative numbers and that no denominators are 0. 3m / 2 + (√m + n)183views
Textbook QuestionConcept Check: By what number should the numerator and denominator of 1/(∛3 - ∛5) be multiplied in order to rationalize the denominator? Write this fraction with a rationalized denominator.349views