02:27Simplify Square Roots of Perfect Squares: Square Root of 81 & (121/144), Negative Square Root of 64Wendy674views
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√3169views
Textbook QuestionDetermine whether each statement is true or false. If false, correct the right side of the equation. (y^2)(y^5) = y^7241views
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 )^1/3321views
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 )^-1/3380views
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 )^-1/3234views
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 )^1/3294views
Textbook QuestionIn Exercises 1–20, use radical notation to rewrite each expression. Simplify, if possible. (-27)^⅓151views
Textbook QuestionIn Exercises 1–20, evaluate each expression, or state that the expression is not a real number. ___ -√ 36166views
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^1/3314views
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^1/3206views
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^-1/3231views
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=11168views
Textbook QuestionIn Exercises 1–20, use radical notation to rewrite each expression. Simplify, if possible. -16^¼169views
Textbook QuestionIn Exercises 1–20, evaluate each expression, or state that the expression is not a real number. ___ √-36166views
Textbook QuestionEvaluate each expression in Exercises 1–12, or indicate that the root is not a real number. √−25331views
Textbook QuestionIn Exercises 1–38, multiply as indicated. If possible, simplify any radical expressions that appear in the product. √6 (4√6 - 3√2)152views
Textbook QuestionIn Exercises 1–20, use radical notation to rewrite each expression. Simplify, if possible. (xy)^⅓151views
Textbook QuestionIn Exercises 1–20, evaluate each expression, or state that the expression is not a real number. ____ √1/25163views
Textbook QuestionPerform the operation and/or simplify each of the following. Assume all variables represent positive real numbers. √50245views
Textbook QuestionEvaluate each expression in Exercises 1–12, or indicate that the root is not a real number. √144+25279views
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^2/9269views
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)165views
Textbook QuestionIn Exercises 1–20, use radical notation to rewrite each expression. Simplify, if possible. (2xy³)^⅕236views
Textbook QuestionIn Exercises 1–20, evaluate each expression, or state that the expression is not a real number. ____ -√9/16164views
Textbook QuestionPerform the operation and/or simplify each of the following. Assume all variables represent positive real numbers. 3√xy - 8√xy207views
Textbook QuestionEvaluate each expression in Exercises 1–12, or indicate that the root is not a real number. √25−√16237views
Textbook QuestionPerform the operation and/or simplify each of the following. Assume all variables represent positive real numbers. (2 + √3) (2 - √3)231views
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. -1/125334views
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)160views
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√x196views
Textbook QuestionIn Exercises 1–20, use radical notation to rewrite each expression. Simplify, if possible. 81^3/2152views
Textbook QuestionIn Exercises 1–20, evaluate each expression, or state that the expression is not a real number. ____ √0.81175views
Textbook QuestionEvaluate each expression in Exercises 1–12, or indicate that the root is not a real number. √(−17)^2260views
Textbook QuestionIn Exercises 1–38, multiply as indicated. If possible, simplify any radical expressions that appear in the product. (7 + √2) (8 + √2)155views
Textbook QuestionIn Exercises 11–28, add or subtract as indicated. You will need to simplify terms to identify the like radicals. _ __ √5 + √20152views
Textbook QuestionIn Exercises 1–20, use the product rule to multiply. ___ _____ ⁶√x-5 ⋅ ⁶√(x-5)⁴168views
Textbook QuestionIn Exercises 1–38, multiply as indicated. If possible, simplify any radical expressions that appear in the product. (4 + √5) (10 - 3√5)164views
Textbook QuestionIn Exercises 11–28, add or subtract as indicated. You will need to simplify terms to identify the like radicals. __ __ 5√12 + √75138views
Textbook QuestionIn Exercises 1–38, solve each radical equation. _____ _____ √6x + 2 = √5x + 3156views
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)161views
Textbook QuestionIn Exercises 11–28, add or subtract as indicated. You will need to simplify terms to identify the like radicals. ___ ___ 5√45x - 2√20x155views
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⋅√ 8x295views
Textbook QuestionIn Exercises 11–28, add or subtract as indicated. You will need to simplify terms to identify the like radicals. __ __ 3³√24 + ³√81157views
Textbook QuestionIn Exercises 1–20, use radical notation to rewrite each expression. Simplify, if possible. (xy)^4/7219views
Textbook QuestionIn Exercises 1–20, evaluate each expression, or state that the expression is not a real number. ______ √16 − 25179views
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^2645views
Textbook QuestionIn Exercises 1–38, solve each radical equation. ____ ____ √x - 4 + √x + 4 = 4176views
Textbook QuestionIn Exercises 1–38, multiply as indicated. If possible, simplify any radical expressions that appear in the product. (√2 + √7)²159views
Textbook QuestionSimplify each expression. Assume all variables represent nonzero real numbers. See Examples 1–3. (6^4)^3237views
Textbook QuestionIn Exercises 25–34, use the zero-exponent rule to simplify each expression. 6⁰176views
Textbook QuestionIn Exercises 21–38, rewrite each expression with rational exponents. ___ ⁵√11x297views
Textbook QuestionIn Exercises 1–38, multiply as indicated. If possible, simplify any radical expressions that appear in the product. (√2x - √y)²152views
Textbook QuestionSimplify each expression. Assume all variables represent nonzero real numbers. See Examples 1–3. (-2x^5)^5239views
Textbook QuestionIn Exercises 11–28, add or subtract as indicated. You will need to simplify terms to identify the like radicals. ______ ___ √4x - 12 + √x-3137views
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^2/3626views
Textbook QuestionIn Exercises 1–38, multiply as indicated. If possible, simplify any radical expressions that appear in the product. (√6 + √2) (√6 - √2)154views
Textbook QuestionSimplify each expression. Assume all variables represent nonzero real numbers. See Examples 1–3. -(2x^0y^4)^3233views
Textbook QuestionIn Exercises 11–28, add or subtract as indicated. You will need to simplify terms to identify the like radicals. ___ ___ 4³√x⁴y² + 5x³√xy²160views
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^5/4371views
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)149views
Textbook QuestionSimplify each expression. Assume all variables represent nonzero real numbers. See Examples 1–3. (p^4/q)^2335views
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)^4/7424views
Textbook QuestionUse the quotient rule to simplify the expressions in Exercises 23–32. Assume that x > 0. √24x^4/√3x569views
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√ k²316views
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)154views
Textbook QuestionSimplify each expression. Assume all variables represent nonzero real numbers. See Examples 1–3. (-5n^4/r^2)^3704views
Textbook QuestionUse the quotient rule to simplify the expressions in Exercises 23–32. Assume that x > 0. √500x^3/√10x^−1272views
Textbook QuestionSimplify each expression. Assume all variables represent nonzero real numbers. See Examples 1–3. -(x^3y^5/z)^0649views
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 √5p³379views
Textbook QuestionIn Exercises 25–34, use the zero-exponent rule to simplify each expression. (13y)⁰258views
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 √2y⁵225views
Textbook QuestionIn Exercises 1–38, solve each radical equation. ____ _____ √x + 2 + √3x + 7 = 1233views
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)²157views
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. -6309views
Textbook QuestionIn Exercises 35–52, write each expression with positive exponents only. Then simplify, if possible. 3⁻²154views
Textbook QuestionIn Exercises 21–38, rewrite each expression with rational exponents. ____ (⁶√7xy² ) ⁵161views
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)³167views
Textbook QuestionIn Exercises 35–52, write each expression with positive exponents only. Then simplify, if possible. (-5)⁻²156views
Textbook QuestionIn Exercises 21–38, rewrite each expression with rational exponents. __ 2x ³√y²164views
Textbook QuestionIn Exercises 33–38, express the function, f, in simplified form. Assume that x can be any real number. ___________ f(x) = √5x² - 10x + 5194views
Textbook QuestionIn Exercises 35–52, write each expression with positive exponents only. Then simplify, if possible. -5⁻²295views
Textbook QuestionIn Exercises 39–54, rewrite each expression with a positive rational exponent. Simplify, if possible. 49^-½166views
Textbook QuestionWrite each expression without negative exponents, and evaluate if possible. Assume all variables represent nonzero real numbers. See Example 4. -5^-4283views
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. __ √x⁵157views
Textbook QuestionIn Exercises 35–52, write each expression with positive exponents only. Then simplify, if possible. x²y⁻³156views
Textbook QuestionIn Exercises 39–54, rewrite each expression with a positive rational exponent. Simplify, if possible. 27^-⅓148views
Textbook QuestionWrite each expression without negative exponents, and evaluate if possible. Assume all variables represent nonzero real numbers. See Example 4. (1/3)^-2233views
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. ___ √x⁶y⁷149views
Textbook QuestionIn Exercises 39–54, rewrite each expression with a positive rational exponent. Simplify, if possible. 16^-¾163views
Textbook QuestionIn Exercises 33–44, add or subtract terms whenever possible. 3√8−√32+3√72−√75310views
Textbook QuestionWrite each expression without negative exponents, and evaluate if possible. Assume all variables represent nonzero real numbers. See Example 4. (4x)^-2493views
Textbook QuestionWrite each expression without negative exponents, and evaluate if possible. Assume all variables represent nonzero real numbers. See Example 4. 4x^-2246views
Textbook QuestionUse the rules for radicals to perform the indicated operations. Assume all variable expressions represent positive real numbers. √7 • √28223views
Textbook QuestionWrite each expression without negative exponents, and evaluate if possible. Assume all variables represent nonzero real numbers. See Example 4. -a^-3251views
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√x³y¹⁷z²185views
Textbook QuestionIn Exercises 35–52, write each expression with positive exponents only. Then simplify, if possible. x⁻²/y⁻⁵162views
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√32x⁹y¹⁷160views
Textbook QuestionIn Exercises 35–52, write each expression with positive exponents only. Then simplify, if possible. a⁻⁴b⁷/c⁻³185views
Textbook QuestionIn Exercises 39–54, rewrite each expression with a positive rational exponent. Simplify, if possible. (2xy)^-7/10190views
Textbook QuestionUse the rules for radicals to perform the indicated operations. Assume all variable expressions represent positive real numbers. ⁵√x² • ⁵√x³297views
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)⁴148views
Textbook QuestionIn Exercises 39–54, rewrite each expression with a positive rational exponent. Simplify, if possible. 5xz^-⅓164views
Textbook QuestionUse the rules for radicals to perform the indicated operations. Assume all variable expressions represent positive real numbers. ∜ m² • ∜ m²235views
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√y¹⁸196views
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^12235views
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)194views
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^-2213views
Textbook QuestionIn Exercises 55–78, use properties of rational exponents to simplify each expression. Assume that all variables represent positive numbers. 3^¾ ⋅ 3^¼164views
Textbook QuestionUse the rules for radicals to perform the indicated operations. Assume all variable expressions represent positive real numbers. √14 • √3pqr351views
Textbook QuestionEvaluate each expression in Exercises 55–66, or indicate that the root is not a real number. ³√8270views
Textbook QuestionIn Exercises 45–66, divide and, if possible, simplify. ______ √54a⁷b¹¹ √3a⁻⁴b⁻²154views
Textbook QuestionIn Exercises 55–58, find the indicated function values for each function. ____ g(x) = −³√8x−8; g(2), g(1), g(0)165views
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^-6244views
Textbook QuestionIn Exercises 55–78, use properties of rational exponents to simplify each expression. Assume that all variables represent positive numbers. 16^¾ 16^¼153views
Textbook QuestionUse the rules for radicals to perform the indicated operations. Assume all variable expressions represent positive real numbers. ∛ 7x • ∛ 2y231views
Textbook QuestionSimplify each exponential expression in Exercises 23–64. 10x^4 y^9/30x^12 y^−3273views
Textbook QuestionIn Exercises 59–72, simplify each expression using the products-to-powers rule. (4x)³148views
Textbook QuestionUse the rules for radicals to perform the indicated operations. Assume all variable expressions represent positive real numbers. √9/25278views
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^-3393views
Textbook QuestionIn Exercises 55–78, use properties of rational exponents to simplify each expression. Assume that all variables represent positive numbers. x^½ ⋅ x^⅓146views
Textbook QuestionEvaluate each expression in Exercises 55–66, or indicate that the root is not a real number. ⁴√−16261views
Textbook QuestionIn Exercises 45–66, divide and, if possible, simplify. ______ ³√250x⁵y³ ³√2x³168views
Textbook QuestionIn Exercises 55–78, use properties of rational exponents to simplify each expression. Assume that all variables represent positive numbers. x^⅘ x^⅕159views
Textbook QuestionUse the rules for radicals to perform the indicated operations. Assume all variable expressions represent positive real numbers. - ∛5/8208views
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)^2261views
Textbook QuestionIn Exercises 45–66, divide and, if possible, simplify. ______ ⁵√96x¹²y¹¹ ⁵√3x²y⁻²156views
Textbook QuestionSimplify the radical expressions in Exercises 58 - 62. ∜(32x^5)/∜(16x) (Assume that x > 0.)314views
Textbook QuestionUse the rules for radicals to perform the indicated operations. Assume all variable expressions represent positive real numbers. ∜m/n⁴319views
Textbook QuestionEvaluate each expression in Exercises 55–66, or indicate that the root is not a real number. ⁵√(−3)^5301views
Textbook QuestionSimplify each exponential expression in Exercises 23–64. (3a^−5 b^2/12a^3 b^−4)^0287views
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)^-3237views
Textbook QuestionIn Exercises 45–66, divide and, if possible, simplify. _______ ³√x²+7x+12 ³√x+3141views
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 ⋅ √10y159views
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^-4212views
Textbook QuestionIn Exercises 59–76, find the indicated root, or state that the expression is not a real number. ___ ⁴√−16154views
Textbook QuestionEvaluate each expression in Exercises 55–66, or indicate that the root is not a real number. ⁶√1/64330views
Textbook QuestionIn Exercises 65–74, simplify each radical expression and then rationalize the denominator. 25 --------- √5x²y149views
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^4461views
Textbook QuestionIn Exercises 59–76, find the indicated root, or state that the expression is not a real number. ___ ⁵√−1175views
Textbook QuestionIn Exercises 59–72, simplify each expression using the products-to-powers rule. (-3x⁻²)⁻³146views
Textbook QuestionUse the rules for radicals to perform the indicated operations. Assume all variable expressions represent positive real numbers. ∜∛2283views
Textbook QuestionIn Exercises 65–74, simplify each radical expression and then rationalize the denominator. 150a³ - √ ---------- b⁵156views
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 ⋅ √10xy²146views
Textbook QuestionUse the rules for radicals to perform the indicated operations. Assume all variable expressions represent positive real numbers. ⁵√∛9265views
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)^-2454views
Textbook QuestionIn Exercises 59–76, find the indicated root, or state that the expression is not a real number. ___ ⁶√−1155views
Textbook QuestionIn Exercises 59–72, simplify each expression using the products-to-powers rule. (5x³y⁻⁴)⁻²153views
Textbook QuestionIn Exercises 55–78, use properties of rational exponents to simplify each expression. Assume that all variables represent positive numbers. (2x^⅕)⁵148views
Textbook QuestionIn Exercises 65–74, simplify each radical expression and then rationalize the denominator. 5m⁴n⁶ √ ------------- 15m³n⁴154views
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√6154views
Textbook QuestionIn Exercises 59–76, find the indicated root, or state that the expression is not a real number. ___ −⁴√256146views
Textbook QuestionIn Exercises 59–72, simplify each expression using the products-to-powers rule. (-2x⁻⁵y⁴z²)⁻⁴152views
Textbook QuestionIn Exercises 55–78, use properties of rational exponents to simplify each expression. Assume that all variables represent positive numbers. (25x⁴y⁶)^½238views
Textbook QuestionSimplify each radical. Assume all variables represent positive real numbers. √192454views
Textbook QuestionIn Exercises 59–76, find the indicated root, or state that the expression is not a real number. __ ⁶√64167views
Textbook QuestionIn Exercises 55–78, use properties of rational exponents to simplify each expression. Assume that all variables represent positive numbers. (x^½y^-⅗)^½156views
Textbook QuestionIn Exercises 73–84, simplify each expression using the quotients-to-powers rule. (2/x)⁴143views
Textbook QuestionSimplify the radical expressions in Exercises 67–74, if possible. ⁵√64x^6/⁵√2x477views
Textbook QuestionIn Exercises 65–74, simplify each radical expression and then rationalize the denominator. 15 ------------ ³√-27x⁴y¹¹152views
Textbook QuestionSimplify each radical. Assume all variables represent positive real numbers. ∛250265views
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 3^¼155views
Textbook QuestionIn Exercises 73–84, simplify each expression using the quotients-to-powers rule. (x³/5)²186views
Textbook QuestionSimplify each radical. Assume all variables represent positive real numbers. - ∜243986views
Textbook QuestionIn Exercises 75–92, rationalize each denominator. Simplify, if possible. 15 ---------- √6 + 1163views
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^1/12278views
Textbook QuestionIn Exercises 73–84, simplify each expression using the quotients-to-powers rule. (- 3x/y)⁴154views
Textbook QuestionIn Exercises 77–90, simplify each expression. Include absolute value bars where necessary. __ ³√x³154views
Textbook QuestionSimplify each radical. Assume all variables represent positive real numbers. -9 ⁵√243273views
Textbook QuestionIn Exercises 75–92, rationalize each denominator. Simplify, if possible. 17 ---------- √10 - 2149views
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√x²158views
Textbook QuestionIn Exercises 77–90, simplify each expression. Include absolute value bars where necessary. __ ⁴√y⁴167views
Textbook QuestionIn Exercises 75–82, add or subtract terms whenever possible. ³√54xy^3−y³√128x265views
Textbook QuestionIn Exercises 75–92, rationalize each denominator. Simplify, if possible. 12 ------------ √7 + √3148views
Textbook QuestionSimplify each radical. Assume all variables represent positive real numbers. ∛(16 (-2)⁴ (2)⁸)298views
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. -8/27248views
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√8a⁶168views
Textbook QuestionIn Exercises 77–90, simplify each expression. Include absolute value bars where necessary. ____ ³√−8x³154views
Textbook QuestionIn Exercises 75–92, rationalize each denominator. Simplify, if possible. √b ---------- √a - √b135views
Textbook QuestionSimplify each expression. Write answers without negative exponents. Assume all vari-ables represent positive real numbers. See Examples 8 and 9. 8^2/3421views
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√x¹⁰y¹⁵152views
Textbook QuestionIn Exercises 77–90, simplify each expression. Include absolute value bars where necessary. ____ ³√(−5)³160views
Textbook QuestionSimplify each radical. Assume all variables represent positive real numbers. √24m⁶n⁵263views
Textbook QuestionSimplify each radical. Assume all variables represent positive real numbers. ∜(x⁴ + y⁴)274views
Textbook QuestionSimplify each radical. Assume all variables represent positive real numbers. ∛(27 + a³)231views
Textbook QuestionSimplify each radical. Assume all variables represent positive real numbers. ⁹√5³255views
Textbook QuestionSimplify each radical. Assume all variables represent positive real numbers. ⁶√11³230views
Textbook QuestionIn Exercises 83–90, evaluate each expression without using a calculator. 16^(−6/2)300views
Textbook QuestionSimplify each radical. Assume all variables represent positive real numbers. ⁸√5⁴288views
Textbook QuestionIn Exercises 75–92, rationalize each denominator. Simplify, if possible. 2√6 + √5 -------------- 3√6 - √5138views
Textbook QuestionSimplify each radical. Assume all variables represent positive real numbers. ⁶√x¹⁸y²678views
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)435views
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√x⁶y³153views
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)274views
Textbook QuestionIn Exercises 93–104, rationalize each numerator. Simplify, if possible. 5 √ --- 3177views
Textbook QuestionSimplify each radical. Assume all variables represent positive real numbers. ⁹√∜7³241views
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)243views
Textbook QuestionPerform the indicated operations. Assume all variables represent positive real numbers. 8√(2x) - √(8x) + √(72x)677views
Textbook QuestionIn Exercises 93–104, rationalize each numerator. Simplify, if possible. ³√2x ³√y152views
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)297views
Textbook QuestionPerform the indicated operations. Assume all variables represent positive real numbers. 3√72m² - 5√32m² - 3√18m²225views
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√ab152views
Textbook QuestionIn Exercises 85–116, simplify each exponential expression. (-¼x⁻⁴y⁵z⁻¹)(-12x⁻³y⁻¹z⁴)155views
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)300views
Textbook QuestionIn Exercises 93–104, rationalize each numerator. Simplify, if possible. √x + 4 √x161views
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^2376views
Textbook QuestionPerform the indicated operations. Assume all variables represent positive real numbers. 2∛3 + 4∛24 - ∛81235views
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√x172views
Textbook QuestionIn Exercises 93–104, rationalize each numerator. Simplify, if possible. √a - √b √a + √b218views
Textbook QuestionPerform the indicated operations. Assume all variables represent positive real numbers. ∜32 + 3∜2227views
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√y159views
Textbook QuestionPerform the indicated operations. Assume all variables represent positive real numbers. 2∛16 + ∛54221views
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√√x153views
Textbook QuestionIn Exercises 103–110, insert either <, >, or = in the shaded area to make a true statement. |−20| □ |−50|270views
Textbook QuestionPerform the indicated operations. Assume all variables represent positive real numbers. 3x∛xy² - 2∛8x⁴y²238views
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. ____ √√x²y155views
Textbook QuestionIn Exercises 85–116, simplify each exponential expression. -24a³b⁻⁵c⁵/-3a⁻⁶b⁻⁴c⁻⁷159views
Textbook QuestionIn Exercises 105–110, use an associative property to write an algebraic expression equivalent to each expression and simplify. 4+(6+x)154views
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)^3329views
Textbook QuestionIn Exercises 103–110, insert either <, >, or = in the shaded area to make a true statement. 30/40−3/4 □ 14/15⋅15/14302views
Textbook QuestionIn Exercises 107–114, simplify each exponential expression. Assume that variables represent nonzero real numbers. (x^−2 y)^−3/(x^2 y^−1)^3331views
Textbook QuestionIn Exercises 101–108, simplify by reducing the index of the radical. ⁹√x^6 y^3304views
Textbook QuestionIn Exercises 101–108, simplify by reducing the index of the radical. ¹²√x^4y^8296views
Textbook QuestionPerform the indicated operations. Assume all variables represent positive real numbers. ∛64xy² + ∛27x⁴y⁵236views
Textbook QuestionIn Exercises 107–114, simplify each exponential expression. Assume that variables represent nonzero real numbers. (3x−4 y z−7)(3x)−3274views
Textbook QuestionIn Exercises 111–114, simplify each expression. Assume that all variables represent positive numbers. (49x^−2y^4)^−1/2(xy^1/2)330views
Textbook QuestionPerform the indicated operations. Assume all variables represent positive real numbers. ∜81x⁶y³ - ∜16x¹⁰y³244views
Textbook QuestionIn Exercises 111–114, simplify each expression. Assume that all variables represent positive numbers. (x^−5/4y^1/3x^−3/4)^−6591views
Textbook QuestionPerform the indicated operations. Assume all variables represent positive real numbers. 5√6 + 2√10287views
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)^2263views
Textbook QuestionPerform the indicated operations. Assume all variables represent positive real numbers. √6(3 + √7)273views
Textbook QuestionIn Exercises 85–116, simplify each exponential expression. (20a⁻³b⁴c⁵/-2a⁻⁵b⁻²c)⁻²145views
Textbook QuestionPerform the indicated operations. Assume all variables represent positive real numbers. 4√3(√7 - 2√11)257views
Textbook QuestionIn Exercises 117–124, simplify each exponential expression. 9y⁴/x⁻² + (x⁻¹/y²)⁻²163views
Textbook QuestionPerform the indicated operations. Assume all variables represent positive real numbers. (√2 + 3) (√2 - 3)213views
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.160views
Textbook QuestionIn Exercises 117–124, simplify each exponential expression. (3x⁴/y⁻⁴)⁻¹(2x/y²)³166views
Textbook QuestionPerform the indicated operations. Assume all variables represent positive real numbers. (∛11 - 1) (∛11² + ∛11 +1)249views
Textbook QuestionIn Exercises 117–124, simplify each exponential expression. (-4x³y⁻⁵)⁻²(2x⁻⁸y⁻⁵)164views
Textbook QuestionIn Exercises 117–124, simplify each exponential expression. (2x²y⁴)⁻¹(4xy³)⁻³ / (x²y)⁻⁵(x³y²)⁴206views
Textbook QuestionPerform the indicated operations. Assume all variables represent positive real numbers. (3√2 + √3) (2√3 - √2)221views
Textbook QuestionPerform the indicated operations and/or simplify each expression. Assume all variables represent positive real numbers. 5/√2223views
Textbook QuestionPerform the indicated operations and/or simplify each expression. Assume all variables represent positive real numbers. ∛2/3276views
Textbook QuestionPerform the indicated operations and/or simplify each expression. Assume all variables represent positive real numbers. ∜2/25231views
Textbook QuestionPerform the indicated operations and/or simplify each expression. Assume all variables represent positive real numbers. √2/3x273views
Textbook QuestionPerform the indicated operations and/or simplify each expression. Assume all variables represent positive real numbers. √(x⁵y³)/z²297views
Textbook QuestionPerform the indicated operations and/or simplify each expression. Assume all variables represent positive real numbers. ∛8/x⁴239views
Textbook QuestionPerform the indicated operations and/or simplify each expression. Assume all variables represent positive real numbers. (∛mn • ∛m²) / ∛n²223views
Textbook QuestionPerform the indicated operations and/or simplify each expression. Assume all variables represent positive real numbers. (-4 /∛3 ) + (1/∛24) - ( 2/∛81)225views
Textbook QuestionPerform the indicated operations and/or simplify each expression. Assume all variables represent positive real numbers. ( 5/∛2) - ( 2/∛16) + (1/∛54)285views
Textbook QuestionRationalize each denominator. Assume all variables represent nonnegative numbers and that no denominators are 0. 1/(2 + √5)281views
Textbook QuestionRationalize each denominator. Assume all variables represent nonnegative numbers and that no denominators are 0. (√7 - 1) / (2√7 + 4√2)333views
Textbook QuestionRationalize each denominator. Assume all variables represent nonnegative numbers and that no denominators are 0. (p - 4) / (√p + 2)346views
Textbook QuestionRationalize each denominator. Assume all variables represent nonnegative numbers and that no denominators are 0. 3m / 2 + (√m + n)176views
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.328views