02:27Simplify Square Roots of Perfect Squares: Square Root of 81 & (121/144), Negative Square Root of 64Wendy694views
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√3175views
Textbook QuestionDetermine whether each statement is true or false. If false, correct the right side of the equation. (y^2)(y^5) = y^7253views
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 )^1/3344views
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 )^-1/3404views
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 )^-1/3246views
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 )^1/3302views
Textbook QuestionIn Exercises 1–20, use radical notation to rewrite each expression. Simplify, if possible. (-27)^⅓162views
Textbook QuestionIn Exercises 1–20, evaluate each expression, or state that the expression is not a real number. ___ -√ 36181views
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^1/3322views
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^1/3213views
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^-1/3243views
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=11177views
Textbook QuestionIn Exercises 1–20, use radical notation to rewrite each expression. Simplify, if possible. -16^¼180views
Textbook QuestionIn Exercises 1–20, evaluate each expression, or state that the expression is not a real number. ___ √-36177views
Textbook QuestionEvaluate each expression in Exercises 1–12, or indicate that the root is not a real number. √−25350views
Textbook QuestionIn Exercises 1–38, multiply as indicated. If possible, simplify any radical expressions that appear in the product. √6 (4√6 - 3√2)164views
Textbook QuestionIn Exercises 1–20, use radical notation to rewrite each expression. Simplify, if possible. (xy)^⅓159views
Textbook QuestionIn Exercises 1–20, evaluate each expression, or state that the expression is not a real number. ____ √1/25180views
Textbook QuestionPerform the operation and/or simplify each of the following. Assume all variables represent positive real numbers. √50256views
Textbook QuestionEvaluate each expression in Exercises 1–12, or indicate that the root is not a real number. √144+25287views
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^2/9275views
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)172views
Textbook QuestionIn Exercises 1–20, use radical notation to rewrite each expression. Simplify, if possible. (2xy³)^⅕251views
Textbook QuestionIn Exercises 1–20, evaluate each expression, or state that the expression is not a real number. ____ -√9/16173views
Textbook QuestionPerform the operation and/or simplify each of the following. Assume all variables represent positive real numbers. 3√xy - 8√xy218views
Textbook QuestionEvaluate each expression in Exercises 1–12, or indicate that the root is not a real number. √25−√16249views
Textbook QuestionPerform the operation and/or simplify each of the following. Assume all variables represent positive real numbers. (2 + √3) (2 - √3)242views
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. -1/125344views
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)167views
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√x202views
Textbook QuestionIn Exercises 1–20, use radical notation to rewrite each expression. Simplify, if possible. 81^3/2163views
Textbook QuestionIn Exercises 1–20, evaluate each expression, or state that the expression is not a real number. ____ √0.81187views
Textbook QuestionEvaluate each expression in Exercises 1–12, or indicate that the root is not a real number. √(−17)^2268views
Textbook QuestionIn Exercises 1–38, multiply as indicated. If possible, simplify any radical expressions that appear in the product. (7 + √2) (8 + √2)165views
Textbook QuestionIn Exercises 11–28, add or subtract as indicated. You will need to simplify terms to identify the like radicals. _ __ √5 + √20160views
Textbook QuestionIn Exercises 1–20, use the product rule to multiply. ___ _____ ⁶√x-5 ⋅ ⁶√(x-5)⁴180views
Textbook QuestionIn Exercises 1–38, multiply as indicated. If possible, simplify any radical expressions that appear in the product. (4 + √5) (10 - 3√5)172views
Textbook QuestionIn Exercises 11–28, add or subtract as indicated. You will need to simplify terms to identify the like radicals. __ __ 5√12 + √75148views
Textbook QuestionIn Exercises 1–38, solve each radical equation. _____ _____ √6x + 2 = √5x + 3165views
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)170views
Textbook QuestionIn Exercises 11–28, add or subtract as indicated. You will need to simplify terms to identify the like radicals. ___ ___ 5√45x - 2√20x162views
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⋅√ 8x308views
Textbook QuestionIn Exercises 11–28, add or subtract as indicated. You will need to simplify terms to identify the like radicals. __ __ 3³√24 + ³√81170views
Textbook QuestionIn Exercises 1–20, use radical notation to rewrite each expression. Simplify, if possible. (xy)^4/7235views
Textbook QuestionIn Exercises 1–20, evaluate each expression, or state that the expression is not a real number. ______ √16 − 25189views
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^2659views
Textbook QuestionIn Exercises 1–38, solve each radical equation. ____ ____ √x - 4 + √x + 4 = 4187views
Textbook QuestionIn Exercises 1–38, multiply as indicated. If possible, simplify any radical expressions that appear in the product. (√2 + √7)²167views
Textbook QuestionSimplify each expression. Assume all variables represent nonzero real numbers. See Examples 1–3. (6^4)^3248views
Textbook QuestionIn Exercises 25–34, use the zero-exponent rule to simplify each expression. 6⁰182views
Textbook QuestionIn Exercises 21–38, rewrite each expression with rational exponents. ___ ⁵√11x313views
Textbook QuestionIn Exercises 1–38, multiply as indicated. If possible, simplify any radical expressions that appear in the product. (√2x - √y)²166views
Textbook QuestionSimplify each expression. Assume all variables represent nonzero real numbers. See Examples 1–3. (-2x^5)^5251views
Textbook QuestionIn Exercises 11–28, add or subtract as indicated. You will need to simplify terms to identify the like radicals. ______ ___ √4x - 12 + √x-3145views
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^2/3652views
Textbook QuestionIn Exercises 1–38, multiply as indicated. If possible, simplify any radical expressions that appear in the product. (√6 + √2) (√6 - √2)167views
Textbook QuestionSimplify each expression. Assume all variables represent nonzero real numbers. See Examples 1–3. -(2x^0y^4)^3244views
Textbook QuestionIn Exercises 11–28, add or subtract as indicated. You will need to simplify terms to identify the like radicals. ___ ___ 4³√x⁴y² + 5x³√xy²168views
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^5/4392views
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)159views
Textbook QuestionSimplify each expression. Assume all variables represent nonzero real numbers. See Examples 1–3. (p^4/q)^2346views
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)^4/7444views
Textbook QuestionUse the quotient rule to simplify the expressions in Exercises 23–32. Assume that x > 0. √24x^4/√3x595views
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√ k²328views
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)161views
Textbook QuestionSimplify each expression. Assume all variables represent nonzero real numbers. See Examples 1–3. (-5n^4/r^2)^3725views
Textbook QuestionUse the quotient rule to simplify the expressions in Exercises 23–32. Assume that x > 0. √500x^3/√10x^−1286views
Textbook QuestionSimplify each expression. Assume all variables represent nonzero real numbers. See Examples 1–3. -(x^3y^5/z)^0697views
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 √5p³398views
Textbook QuestionIn Exercises 25–34, use the zero-exponent rule to simplify each expression. (13y)⁰279views
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 √2y⁵235views
Textbook QuestionIn Exercises 1–38, solve each radical equation. ____ _____ √x + 2 + √3x + 7 = 1245views
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)²162views
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. -6326views
Textbook QuestionIn Exercises 35–52, write each expression with positive exponents only. Then simplify, if possible. 3⁻²165views
Textbook QuestionIn Exercises 21–38, rewrite each expression with rational exponents. ____ (⁶√7xy² ) ⁵171views
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)³175views
Textbook QuestionIn Exercises 35–52, write each expression with positive exponents only. Then simplify, if possible. (-5)⁻²166views
Textbook QuestionIn Exercises 21–38, rewrite each expression with rational exponents. __ 2x ³√y²172views
Textbook QuestionIn Exercises 33–38, express the function, f, in simplified form. Assume that x can be any real number. ___________ f(x) = √5x² - 10x + 5200views
Textbook QuestionIn Exercises 35–52, write each expression with positive exponents only. Then simplify, if possible. -5⁻²309views
Textbook QuestionIn Exercises 39–54, rewrite each expression with a positive rational exponent. Simplify, if possible. 49^-½177views
Textbook QuestionWrite each expression without negative exponents, and evaluate if possible. Assume all variables represent nonzero real numbers. See Example 4. -5^-4293views
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. __ √x⁵169views
Textbook QuestionIn Exercises 35–52, write each expression with positive exponents only. Then simplify, if possible. x²y⁻³164views
Textbook QuestionIn Exercises 39–54, rewrite each expression with a positive rational exponent. Simplify, if possible. 27^-⅓159views
Textbook QuestionWrite each expression without negative exponents, and evaluate if possible. Assume all variables represent nonzero real numbers. See Example 4. (1/3)^-2241views
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. ___ √x⁶y⁷155views
Textbook QuestionIn Exercises 39–54, rewrite each expression with a positive rational exponent. Simplify, if possible. 16^-¾179views
Textbook QuestionIn Exercises 33–44, add or subtract terms whenever possible. 3√8−√32+3√72−√75317views
Textbook QuestionWrite each expression without negative exponents, and evaluate if possible. Assume all variables represent nonzero real numbers. See Example 4. (4x)^-2514views
Textbook QuestionWrite each expression without negative exponents, and evaluate if possible. Assume all variables represent nonzero real numbers. See Example 4. 4x^-2257views
Textbook QuestionUse the rules for radicals to perform the indicated operations. Assume all variable expressions represent positive real numbers. √7 • √28237views
Textbook QuestionWrite each expression without negative exponents, and evaluate if possible. Assume all variables represent nonzero real numbers. See Example 4. -a^-3258views
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√x³y¹⁷z²193views
Textbook QuestionIn Exercises 35–52, write each expression with positive exponents only. Then simplify, if possible. x⁻²/y⁻⁵169views
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√32x⁹y¹⁷173views
Textbook QuestionIn Exercises 35–52, write each expression with positive exponents only. Then simplify, if possible. a⁻⁴b⁷/c⁻³195views
Textbook QuestionIn Exercises 39–54, rewrite each expression with a positive rational exponent. Simplify, if possible. (2xy)^-7/10203views
Textbook QuestionUse the rules for radicals to perform the indicated operations. Assume all variable expressions represent positive real numbers. ⁵√x² • ⁵√x³311views
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)⁴158views
Textbook QuestionIn Exercises 39–54, rewrite each expression with a positive rational exponent. Simplify, if possible. 5xz^-⅓173views
Textbook QuestionUse the rules for radicals to perform the indicated operations. Assume all variable expressions represent positive real numbers. ∜ m² • ∜ m²249views
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√y¹⁸208views
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^12245views
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)207views
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^-2224views
Textbook QuestionIn Exercises 55–78, use properties of rational exponents to simplify each expression. Assume that all variables represent positive numbers. 3^¾ ⋅ 3^¼173views
Textbook QuestionUse the rules for radicals to perform the indicated operations. Assume all variable expressions represent positive real numbers. √14 • √3pqr373views
Textbook QuestionEvaluate each expression in Exercises 55–66, or indicate that the root is not a real number. ³√8281views
Textbook QuestionIn Exercises 45–66, divide and, if possible, simplify. ______ √54a⁷b¹¹ √3a⁻⁴b⁻²161views
Textbook QuestionIn Exercises 55–58, find the indicated function values for each function. ____ g(x) = −³√8x−8; g(2), g(1), g(0)174views
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^-6250views
Textbook QuestionIn Exercises 55–78, use properties of rational exponents to simplify each expression. Assume that all variables represent positive numbers. 16^¾ 16^¼161views
Textbook QuestionUse the rules for radicals to perform the indicated operations. Assume all variable expressions represent positive real numbers. ∛ 7x • ∛ 2y241views
Textbook QuestionSimplify each exponential expression in Exercises 23–64. 10x^4 y^9/30x^12 y^−3282views
Textbook QuestionIn Exercises 59–72, simplify each expression using the products-to-powers rule. (4x)³155views
Textbook QuestionUse the rules for radicals to perform the indicated operations. Assume all variable expressions represent positive real numbers. √9/25283views
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^-3438views
Textbook QuestionIn Exercises 55–78, use properties of rational exponents to simplify each expression. Assume that all variables represent positive numbers. x^½ ⋅ x^⅓158views
Textbook QuestionEvaluate each expression in Exercises 55–66, or indicate that the root is not a real number. ⁴√−16271views
Textbook QuestionIn Exercises 45–66, divide and, if possible, simplify. ______ ³√250x⁵y³ ³√2x³179views
Textbook QuestionIn Exercises 55–78, use properties of rational exponents to simplify each expression. Assume that all variables represent positive numbers. x^⅘ x^⅕166views
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)^2273views
Textbook QuestionIn Exercises 45–66, divide and, if possible, simplify. ______ ⁵√96x¹²y¹¹ ⁵√3x²y⁻²165views
Textbook QuestionSimplify the radical expressions in Exercises 58 - 62. ∜(32x^5)/∜(16x) (Assume that x > 0.)322views
Textbook QuestionUse the rules for radicals to perform the indicated operations. Assume all variable expressions represent positive real numbers. ∜m/n⁴337views
Textbook QuestionEvaluate each expression in Exercises 55–66, or indicate that the root is not a real number. ⁵√(−3)^5311views
Textbook QuestionSimplify each exponential expression in Exercises 23–64. (3a^−5 b^2/12a^3 b^−4)^0300views
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)^-3242views
Textbook QuestionIn Exercises 45–66, divide and, if possible, simplify. _______ ³√x²+7x+12 ³√x+3150views
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 ⋅ √10y168views
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√−16163views
Textbook QuestionEvaluate each expression in Exercises 55–66, or indicate that the root is not a real number. ⁶√1/64342views
Textbook QuestionIn Exercises 65–74, simplify each radical expression and then rationalize the denominator. 25 --------- √5x²y161views
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^4482views
Textbook QuestionIn Exercises 59–76, find the indicated root, or state that the expression is not a real number. ___ ⁵√−1185views
Textbook QuestionIn Exercises 59–72, simplify each expression using the products-to-powers rule. (-3x⁻²)⁻³156views
Textbook QuestionUse the rules for radicals to perform the indicated operations. Assume all variable expressions represent positive real numbers. ∜∛2289views
Textbook QuestionIn Exercises 65–74, simplify each radical expression and then rationalize the denominator. 150a³ - √ ---------- b⁵166views
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 ⋅ √10xy²152views
Textbook QuestionUse the rules for radicals to perform the indicated operations. Assume all variable expressions represent positive real numbers. ⁵√∛9275views
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)^-2474views
Textbook QuestionIn Exercises 59–76, find the indicated root, or state that the expression is not a real number. ___ ⁶√−1163views
Textbook QuestionIn Exercises 59–72, simplify each expression using the products-to-powers rule. (5x³y⁻⁴)⁻²163views
Textbook QuestionIn Exercises 55–78, use properties of rational exponents to simplify each expression. Assume that all variables represent positive numbers. (2x^⅕)⁵153views
Textbook QuestionIn Exercises 65–74, simplify each radical expression and then rationalize the denominator. 5m⁴n⁶ √ ------------- 15m³n⁴164views
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√6168views
Textbook QuestionIn Exercises 59–76, find the indicated root, or state that the expression is not a real number. ___ −⁴√256159views
Textbook QuestionIn Exercises 59–72, simplify each expression using the products-to-powers rule. (-2x⁻⁵y⁴z²)⁻⁴159views
Textbook QuestionIn Exercises 55–78, use properties of rational exponents to simplify each expression. Assume that all variables represent positive numbers. (25x⁴y⁶)^½259views
Textbook QuestionSimplify each radical. Assume all variables represent positive real numbers. √192475views
Textbook QuestionIn Exercises 59–76, find the indicated root, or state that the expression is not a real number. __ ⁶√64178views
Textbook QuestionIn Exercises 55–78, use properties of rational exponents to simplify each expression. Assume that all variables represent positive numbers. (x^½y^-⅗)^½166views
Textbook QuestionIn Exercises 73–84, simplify each expression using the quotients-to-powers rule. (2/x)⁴151views
Textbook QuestionSimplify the radical expressions in Exercises 67–74, if possible. ⁵√64x^6/⁵√2x488views
Textbook QuestionIn Exercises 65–74, simplify each radical expression and then rationalize the denominator. 15 ------------ ³√-27x⁴y¹¹159views
Textbook QuestionSimplify each radical. Assume all variables represent positive real numbers. ∛250276views
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 3^¼162views
Textbook QuestionIn Exercises 73–84, simplify each expression using the quotients-to-powers rule. (x³/5)²196views
Textbook QuestionSimplify each radical. Assume all variables represent positive real numbers. - ∜2431028views
Textbook QuestionIn Exercises 75–92, rationalize each denominator. Simplify, if possible. 15 ---------- √6 + 1183views
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^1/12295views
Textbook QuestionIn Exercises 73–84, simplify each expression using the quotients-to-powers rule. (- 3x/y)⁴161views
Textbook QuestionIn Exercises 77–90, simplify each expression. Include absolute value bars where necessary. __ ³√x³164views
Textbook QuestionSimplify each radical. Assume all variables represent positive real numbers. -9 ⁵√243280views
Textbook QuestionIn Exercises 75–92, rationalize each denominator. Simplify, if possible. 17 ---------- √10 - 2154views
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√x²169views
Textbook QuestionIn Exercises 77–90, simplify each expression. Include absolute value bars where necessary. __ ⁴√y⁴175views
Textbook QuestionIn Exercises 75–82, add or subtract terms whenever possible. ³√54xy^3−y³√128x274views
Textbook QuestionIn Exercises 75–92, rationalize each denominator. Simplify, if possible. 12 ------------ √7 + √3153views
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. -8/27259views
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√8a⁶176views
Textbook QuestionIn Exercises 77–90, simplify each expression. Include absolute value bars where necessary. ____ ³√−8x³166views
Textbook QuestionIn Exercises 75–92, rationalize each denominator. Simplify, if possible. √b ---------- √a - √b149views
Textbook QuestionSimplify each expression. Write answers without negative exponents. Assume all vari-ables represent positive real numbers. See Examples 8 and 9. 8^2/3438views
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√x¹⁰y¹⁵158views
Textbook QuestionIn Exercises 77–90, simplify each expression. Include absolute value bars where necessary. ____ ³√(−5)³166views
Textbook QuestionSimplify each radical. Assume all variables represent positive real numbers. √24m⁶n⁵274views
Textbook QuestionSimplify each radical. Assume all variables represent positive real numbers. ∜(x⁴ + y⁴)287views
Textbook QuestionSimplify each radical. Assume all variables represent positive real numbers. ∛(27 + a³)240views
Textbook QuestionSimplify each radical. Assume all variables represent positive real numbers. ⁹√5³265views
Textbook QuestionSimplify each radical. Assume all variables represent positive real numbers. ⁶√11³245views
Textbook QuestionIn Exercises 83–90, evaluate each expression without using a calculator. 16^(−6/2)308views
Textbook QuestionSimplify each radical. Assume all variables represent positive real numbers. ⁸√5⁴299views
Textbook QuestionIn Exercises 75–92, rationalize each denominator. Simplify, if possible. 2√6 + √5 -------------- 3√6 - √5147views
Textbook QuestionSimplify each radical. Assume all variables represent positive real numbers. ⁶√x¹⁸y²699views
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)458views
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√x⁶y³163views
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)279views
Textbook QuestionIn Exercises 93–104, rationalize each numerator. Simplify, if possible. 5 √ --- 3185views
Textbook QuestionSimplify each radical. Assume all variables represent positive real numbers. ⁹√∜7³251views
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)254views
Textbook QuestionPerform the indicated operations. Assume all variables represent positive real numbers. 8√(2x) - √(8x) + √(72x)704views
Textbook QuestionIn Exercises 93–104, rationalize each numerator. Simplify, if possible. ³√2x ³√y162views
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)309views
Textbook QuestionPerform the indicated operations. Assume all variables represent positive real numbers. 3√72m² - 5√32m² - 3√18m²236views
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√ab162views
Textbook QuestionIn Exercises 85–116, simplify each exponential expression. (-¼x⁻⁴y⁵z⁻¹)(-12x⁻³y⁻¹z⁴)164views
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)309views
Textbook QuestionIn Exercises 93–104, rationalize each numerator. Simplify, if possible. √x + 4 √x169views
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^2395views
Textbook QuestionPerform the indicated operations. Assume all variables represent positive real numbers. 2∛3 + 4∛24 - ∛81245views
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√x182views
Textbook QuestionIn Exercises 93–104, rationalize each numerator. Simplify, if possible. √a - √b √a + √b228views
Textbook QuestionPerform the indicated operations. Assume all variables represent positive real numbers. ∜32 + 3∜2238views
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√y169views
Textbook QuestionPerform the indicated operations. Assume all variables represent positive real numbers. 2∛16 + ∛54230views
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√√x161views
Textbook QuestionIn Exercises 103–110, insert either <, >, or = in the shaded area to make a true statement. |−20| □ |−50|281views
Textbook QuestionPerform the indicated operations. Assume all variables represent positive real numbers. 3x∛xy² - 2∛8x⁴y²251views
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. ____ √√x²y163views
Textbook QuestionIn Exercises 85–116, simplify each exponential expression. -24a³b⁻⁵c⁵/-3a⁻⁶b⁻⁴c⁻⁷169views
Textbook QuestionIn Exercises 105–110, use an associative property to write an algebraic expression equivalent to each expression and simplify. 4+(6+x)160views
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)^3346views
Textbook QuestionIn Exercises 103–110, insert either <, >, or = in the shaded area to make a true statement. 30/40−3/4 □ 14/15⋅15/14311views
Textbook QuestionIn Exercises 107–114, simplify each exponential expression. Assume that variables represent nonzero real numbers. (x^−2 y)^−3/(x^2 y^−1)^3345views
Textbook QuestionIn Exercises 101–108, simplify by reducing the index of the radical. ⁹√x^6 y^3309views
Textbook QuestionIn Exercises 101–108, simplify by reducing the index of the radical. ¹²√x^4y^8301views
Textbook QuestionPerform the indicated operations. Assume all variables represent positive real numbers. ∛64xy² + ∛27x⁴y⁵246views
Textbook QuestionIn Exercises 107–114, simplify each exponential expression. Assume that variables represent nonzero real numbers. (3x−4 y z−7)(3x)−3284views
Textbook QuestionIn Exercises 111–114, simplify each expression. Assume that all variables represent positive numbers. (49x^−2y^4)^−1/2(xy^1/2)341views
Textbook QuestionPerform the indicated operations. Assume all variables represent positive real numbers. ∜81x⁶y³ - ∜16x¹⁰y³254views
Textbook QuestionIn Exercises 111–114, simplify each expression. Assume that all variables represent positive numbers. (x^−5/4y^1/3x^−3/4)^−6615views
Textbook QuestionPerform the indicated operations. Assume all variables represent positive real numbers. 5√6 + 2√10308views
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)^2272views
Textbook QuestionPerform the indicated operations. Assume all variables represent positive real numbers. √6(3 + √7)279views
Textbook QuestionIn Exercises 85–116, simplify each exponential expression. (20a⁻³b⁴c⁵/-2a⁻⁵b⁻²c)⁻²156views
Textbook QuestionPerform the indicated operations. Assume all variables represent positive real numbers. 4√3(√7 - 2√11)266views
Textbook QuestionIn Exercises 117–124, simplify each exponential expression. 9y⁴/x⁻² + (x⁻¹/y²)⁻²172views
Textbook QuestionPerform the indicated operations. Assume all variables represent positive real numbers. (√2 + 3) (√2 - 3)221views
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.169views
Textbook QuestionIn Exercises 117–124, simplify each exponential expression. (3x⁴/y⁻⁴)⁻¹(2x/y²)³179views
Textbook QuestionPerform the indicated operations. Assume all variables represent positive real numbers. (∛11 - 1) (∛11² + ∛11 +1)260views
Textbook QuestionIn Exercises 117–124, simplify each exponential expression. (-4x³y⁻⁵)⁻²(2x⁻⁸y⁻⁵)174views
Textbook QuestionIn Exercises 117–124, simplify each exponential expression. (2x²y⁴)⁻¹(4xy³)⁻³ / (x²y)⁻⁵(x³y²)⁴229views
Textbook QuestionPerform the indicated operations. Assume all variables represent positive real numbers. (3√2 + √3) (2√3 - √2)236views
Textbook QuestionPerform the indicated operations and/or simplify each expression. Assume all variables represent positive real numbers. 5/√2231views
Textbook QuestionPerform the indicated operations and/or simplify each expression. Assume all variables represent positive real numbers. ∛2/3287views
Textbook QuestionPerform the indicated operations and/or simplify each expression. Assume all variables represent positive real numbers. ∜2/25245views
Textbook QuestionPerform the indicated operations and/or simplify each expression. Assume all variables represent positive real numbers. √2/3x281views
Textbook QuestionPerform the indicated operations and/or simplify each expression. Assume all variables represent positive real numbers. √(x⁵y³)/z²307views
Textbook QuestionPerform the indicated operations and/or simplify each expression. Assume all variables represent positive real numbers. ∛8/x⁴248views
Textbook QuestionPerform the indicated operations and/or simplify each expression. Assume all variables represent positive real numbers. (∛mn • ∛m²) / ∛n²230views
Textbook QuestionPerform the indicated operations and/or simplify each expression. Assume all variables represent positive real numbers. (-4 /∛3 ) + (1/∛24) - ( 2/∛81)234views
Textbook QuestionPerform the indicated operations and/or simplify each expression. Assume all variables represent positive real numbers. ( 5/∛2) - ( 2/∛16) + (1/∛54)294views
Textbook QuestionRationalize each denominator. Assume all variables represent nonnegative numbers and that no denominators are 0. 1/(2 + √5)295views
Textbook QuestionRationalize each denominator. Assume all variables represent nonnegative numbers and that no denominators are 0. (√7 - 1) / (2√7 + 4√2)349views
Textbook QuestionRationalize each denominator. Assume all variables represent nonnegative numbers and that no denominators are 0. (p - 4) / (√p + 2)356views
Textbook QuestionRationalize each denominator. Assume all variables represent nonnegative numbers and that no denominators are 0. 3m / 2 + (√m + n)185views
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.353views