02:27Simplify Square Roots of Perfect Squares: Square Root of 81 & (121/144), Negative Square Root of 64Wendy681views
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√3170views
Textbook QuestionDetermine whether each statement is true or false. If false, correct the right side of the equation. (y^2)(y^5) = y^7243views
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 )^1/3326views
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 )^-1/3384views
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 )^-1/3236views
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 )^1/3297views
Textbook QuestionIn Exercises 1–20, use radical notation to rewrite each expression. Simplify, if possible. (-27)^⅓155views
Textbook QuestionIn Exercises 1–20, evaluate each expression, or state that the expression is not a real number. ___ -√ 36168views
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^1/3316views
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^1/3207views
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^-1/3235views
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=11171views
Textbook QuestionIn Exercises 1–20, use radical notation to rewrite each expression. Simplify, if possible. -16^¼173views
Textbook QuestionIn Exercises 1–20, evaluate each expression, or state that the expression is not a real number. ___ √-36169views
Textbook QuestionEvaluate each expression in Exercises 1–12, or indicate that the root is not a real number. √−25339views
Textbook QuestionIn Exercises 1–38, multiply as indicated. If possible, simplify any radical expressions that appear in the product. √6 (4√6 - 3√2)154views
Textbook QuestionIn Exercises 1–20, use radical notation to rewrite each expression. Simplify, if possible. (xy)^⅓153views
Textbook QuestionIn Exercises 1–20, evaluate each expression, or state that the expression is not a real number. ____ √1/25168views
Textbook QuestionPerform the operation and/or simplify each of the following. Assume all variables represent positive real numbers. √50248views
Textbook QuestionEvaluate each expression in Exercises 1–12, or indicate that the root is not a real number. √144+25282views
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^2/9270views
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)167views
Textbook QuestionIn Exercises 1–20, use radical notation to rewrite each expression. Simplify, if possible. (2xy³)^⅕241views
Textbook QuestionIn Exercises 1–20, evaluate each expression, or state that the expression is not a real number. ____ -√9/16166views
Textbook QuestionPerform the operation and/or simplify each of the following. Assume all variables represent positive real numbers. 3√xy - 8√xy211views
Textbook QuestionEvaluate each expression in Exercises 1–12, or indicate that the root is not a real number. √25−√16238views
Textbook QuestionPerform the operation and/or simplify each of the following. Assume all variables represent positive real numbers. (2 + √3) (2 - √3)233views
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. -1/125339views
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)162views
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√x198views
Textbook QuestionIn Exercises 1–20, use radical notation to rewrite each expression. Simplify, if possible. 81^3/2154views
Textbook QuestionIn Exercises 1–20, evaluate each expression, or state that the expression is not a real number. ____ √0.81177views
Textbook QuestionEvaluate each expression in Exercises 1–12, or indicate that the root is not a real number. √(−17)^2261views
Textbook QuestionIn Exercises 1–38, multiply as indicated. If possible, simplify any radical expressions that appear in the product. (7 + √2) (8 + √2)157views
Textbook QuestionIn Exercises 11–28, add or subtract as indicated. You will need to simplify terms to identify the like radicals. _ __ √5 + √20154views
Textbook QuestionIn Exercises 1–20, use the product rule to multiply. ___ _____ ⁶√x-5 ⋅ ⁶√(x-5)⁴172views
Textbook QuestionIn Exercises 1–38, multiply as indicated. If possible, simplify any radical expressions that appear in the product. (4 + √5) (10 - 3√5)167views
Textbook QuestionIn Exercises 11–28, add or subtract as indicated. You will need to simplify terms to identify the like radicals. __ __ 5√12 + √75142views
Textbook QuestionIn Exercises 1–38, solve each radical equation. _____ _____ √6x + 2 = √5x + 3159views
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)162views
Textbook QuestionIn Exercises 11–28, add or subtract as indicated. You will need to simplify terms to identify the like radicals. ___ ___ 5√45x - 2√20x157views
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⋅√ 8x297views
Textbook QuestionIn Exercises 11–28, add or subtract as indicated. You will need to simplify terms to identify the like radicals. __ __ 3³√24 + ³√81159views
Textbook QuestionIn Exercises 1–20, use radical notation to rewrite each expression. Simplify, if possible. (xy)^4/7226views
Textbook QuestionIn Exercises 1–20, evaluate each expression, or state that the expression is not a real number. ______ √16 − 25181views
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^2649views
Textbook QuestionIn Exercises 1–38, solve each radical equation. ____ ____ √x - 4 + √x + 4 = 4180views
Textbook QuestionIn Exercises 1–38, multiply as indicated. If possible, simplify any radical expressions that appear in the product. (√2 + √7)²160views
Textbook QuestionSimplify each expression. Assume all variables represent nonzero real numbers. See Examples 1–3. (6^4)^3239views
Textbook QuestionIn Exercises 25–34, use the zero-exponent rule to simplify each expression. 6⁰177views
Textbook QuestionIn Exercises 21–38, rewrite each expression with rational exponents. ___ ⁵√11x304views
Textbook QuestionIn Exercises 1–38, multiply as indicated. If possible, simplify any radical expressions that appear in the product. (√2x - √y)²154views
Textbook QuestionSimplify each expression. Assume all variables represent nonzero real numbers. See Examples 1–3. (-2x^5)^5241views
Textbook QuestionIn Exercises 11–28, add or subtract as indicated. You will need to simplify terms to identify the like radicals. ______ ___ √4x - 12 + √x-3139views
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^2/3637views
Textbook QuestionIn Exercises 1–38, multiply as indicated. If possible, simplify any radical expressions that appear in the product. (√6 + √2) (√6 - √2)157views
Textbook QuestionSimplify each expression. Assume all variables represent nonzero real numbers. See Examples 1–3. -(2x^0y^4)^3235views
Textbook QuestionIn Exercises 11–28, add or subtract as indicated. You will need to simplify terms to identify the like radicals. ___ ___ 4³√x⁴y² + 5x³√xy²162views
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^5/4376views
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)151views
Textbook QuestionSimplify each expression. Assume all variables represent nonzero real numbers. See Examples 1–3. (p^4/q)^2338views
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)^4/7428views
Textbook QuestionUse the quotient rule to simplify the expressions in Exercises 23–32. Assume that x > 0. √24x^4/√3x576views
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√ k²319views
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)155views
Textbook QuestionSimplify each expression. Assume all variables represent nonzero real numbers. See Examples 1–3. (-5n^4/r^2)^3711views
Textbook QuestionUse the quotient rule to simplify the expressions in Exercises 23–32. Assume that x > 0. √500x^3/√10x^−1274views
Textbook QuestionSimplify each expression. Assume all variables represent nonzero real numbers. See Examples 1–3. -(x^3y^5/z)^0662views
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 √5p³384views
Textbook QuestionIn Exercises 25–34, use the zero-exponent rule to simplify each expression. (13y)⁰263views
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 √2y⁵226views
Textbook QuestionIn Exercises 1–38, solve each radical equation. ____ _____ √x + 2 + √3x + 7 = 1235views
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)²158views
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. -6314views
Textbook QuestionIn Exercises 35–52, write each expression with positive exponents only. Then simplify, if possible. 3⁻²158views
Textbook QuestionIn Exercises 21–38, rewrite each expression with rational exponents. ____ (⁶√7xy² ) ⁵162views
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)³169views
Textbook QuestionIn Exercises 35–52, write each expression with positive exponents only. Then simplify, if possible. (-5)⁻²158views
Textbook QuestionIn Exercises 21–38, rewrite each expression with rational exponents. __ 2x ³√y²166views
Textbook QuestionIn Exercises 33–38, express the function, f, in simplified form. Assume that x can be any real number. ___________ f(x) = √5x² - 10x + 5196views
Textbook QuestionIn Exercises 35–52, write each expression with positive exponents only. Then simplify, if possible. -5⁻²300views
Textbook QuestionIn Exercises 39–54, rewrite each expression with a positive rational exponent. Simplify, if possible. 49^-½171views
Textbook QuestionWrite each expression without negative exponents, and evaluate if possible. Assume all variables represent nonzero real numbers. See Example 4. -5^-4285views
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. __ √x⁵159views
Textbook QuestionIn Exercises 35–52, write each expression with positive exponents only. Then simplify, if possible. x²y⁻³158views
Textbook QuestionIn Exercises 39–54, rewrite each expression with a positive rational exponent. Simplify, if possible. 27^-⅓150views
Textbook QuestionWrite each expression without negative exponents, and evaluate if possible. Assume all variables represent nonzero real numbers. See Example 4. (1/3)^-2235views
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. ___ √x⁶y⁷150views
Textbook QuestionIn Exercises 39–54, rewrite each expression with a positive rational exponent. Simplify, if possible. 16^-¾167views
Textbook QuestionIn Exercises 33–44, add or subtract terms whenever possible. 3√8−√32+3√72−√75313views
Textbook QuestionWrite each expression without negative exponents, and evaluate if possible. Assume all variables represent nonzero real numbers. See Example 4. (4x)^-2499views
Textbook QuestionWrite each expression without negative exponents, and evaluate if possible. Assume all variables represent nonzero real numbers. See Example 4. 4x^-2249views
Textbook QuestionUse the rules for radicals to perform the indicated operations. Assume all variable expressions represent positive real numbers. √7 • √28226views
Textbook QuestionWrite each expression without negative exponents, and evaluate if possible. Assume all variables represent nonzero real numbers. See Example 4. -a^-3253views
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√x³y¹⁷z²187views
Textbook QuestionIn Exercises 35–52, write each expression with positive exponents only. Then simplify, if possible. x⁻²/y⁻⁵164views
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√32x⁹y¹⁷162views
Textbook QuestionIn Exercises 35–52, write each expression with positive exponents only. Then simplify, if possible. a⁻⁴b⁷/c⁻³188views
Textbook QuestionIn Exercises 39–54, rewrite each expression with a positive rational exponent. Simplify, if possible. (2xy)^-7/10196views
Textbook QuestionUse the rules for radicals to perform the indicated operations. Assume all variable expressions represent positive real numbers. ⁵√x² • ⁵√x³299views
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)⁴150views
Textbook QuestionIn Exercises 39–54, rewrite each expression with a positive rational exponent. Simplify, if possible. 5xz^-⅓166views
Textbook QuestionUse the rules for radicals to perform the indicated operations. Assume all variable expressions represent positive real numbers. ∜ m² • ∜ m²237views
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√y¹⁸198views
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^12238views
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)199views
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^-2218views
Textbook QuestionIn Exercises 55–78, use properties of rational exponents to simplify each expression. Assume that all variables represent positive numbers. 3^¾ ⋅ 3^¼166views
Textbook QuestionUse the rules for radicals to perform the indicated operations. Assume all variable expressions represent positive real numbers. √14 • √3pqr358views
Textbook QuestionEvaluate each expression in Exercises 55–66, or indicate that the root is not a real number. ³√8272views
Textbook QuestionIn Exercises 45–66, divide and, if possible, simplify. ______ √54a⁷b¹¹ √3a⁻⁴b⁻²157views
Textbook QuestionIn Exercises 55–58, find the indicated function values for each function. ____ g(x) = −³√8x−8; g(2), g(1), g(0)167views
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 16^¼155views
Textbook QuestionUse the rules for radicals to perform the indicated operations. Assume all variable expressions represent positive real numbers. ∛ 7x • ∛ 2y234views
Textbook QuestionSimplify each exponential expression in Exercises 23–64. 10x^4 y^9/30x^12 y^−3275views
Textbook QuestionIn Exercises 59–72, simplify each expression using the products-to-powers rule. (4x)³151views
Textbook QuestionUse the rules for radicals to perform the indicated operations. Assume all variable expressions represent positive real numbers. √9/25279views
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^-3406views
Textbook QuestionIn Exercises 55–78, use properties of rational exponents to simplify each expression. Assume that all variables represent positive numbers. x^½ ⋅ x^⅓150views
Textbook QuestionEvaluate each expression in Exercises 55–66, or indicate that the root is not a real number. ⁴√−16264views
Textbook QuestionIn Exercises 45–66, divide and, if possible, simplify. ______ ³√250x⁵y³ ³√2x³169views
Textbook QuestionIn Exercises 55–78, use properties of rational exponents to simplify each expression. Assume that all variables represent positive numbers. x^⅘ x^⅕162views
Textbook QuestionUse the rules for radicals to perform the indicated operations. Assume all variable expressions represent positive real numbers. - ∛5/8210views
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)^2265views
Textbook QuestionIn Exercises 45–66, divide and, if possible, simplify. ______ ⁵√96x¹²y¹¹ ⁵√3x²y⁻²157views
Textbook QuestionSimplify the radical expressions in Exercises 58 - 62. ∜(32x^5)/∜(16x) (Assume that x > 0.)316views
Textbook QuestionUse the rules for radicals to perform the indicated operations. Assume all variable expressions represent positive real numbers. ∜m/n⁴325views
Textbook QuestionEvaluate each expression in Exercises 55–66, or indicate that the root is not a real number. ⁵√(−3)^5302views
Textbook QuestionSimplify each exponential expression in Exercises 23–64. (3a^−5 b^2/12a^3 b^−4)^0291views
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)^-3238views
Textbook QuestionIn Exercises 45–66, divide and, if possible, simplify. _______ ³√x²+7x+12 ³√x+3142views
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 ⋅ √10y161views
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^-4213views
Textbook QuestionIn Exercises 59–76, find the indicated root, or state that the expression is not a real number. ___ ⁴√−16156views
Textbook QuestionEvaluate each expression in Exercises 55–66, or indicate that the root is not a real number. ⁶√1/64333views
Textbook QuestionIn Exercises 65–74, simplify each radical expression and then rationalize the denominator. 25 --------- √5x²y151views
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^4469views
Textbook QuestionIn Exercises 59–76, find the indicated root, or state that the expression is not a real number. ___ ⁵√−1177views
Textbook QuestionIn Exercises 59–72, simplify each expression using the products-to-powers rule. (-3x⁻²)⁻³149views
Textbook QuestionUse the rules for radicals to perform the indicated operations. Assume all variable expressions represent positive real numbers. ∜∛2284views
Textbook QuestionIn Exercises 65–74, simplify each radical expression and then rationalize the denominator. 150a³ - √ ---------- b⁵160views
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 ⋅ √10xy²147views
Textbook QuestionUse the rules for radicals to perform the indicated operations. Assume all variable expressions represent positive real numbers. ⁵√∛9268views
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)^-2460views
Textbook QuestionIn Exercises 59–76, find the indicated root, or state that the expression is not a real number. ___ ⁶√−1157views
Textbook QuestionIn Exercises 59–72, simplify each expression using the products-to-powers rule. (5x³y⁻⁴)⁻²155views
Textbook QuestionIn Exercises 55–78, use properties of rational exponents to simplify each expression. Assume that all variables represent positive numbers. (2x^⅕)⁵150views
Textbook QuestionIn Exercises 65–74, simplify each radical expression and then rationalize the denominator. 5m⁴n⁶ √ ------------- 15m³n⁴156views
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√6157views
Textbook QuestionIn Exercises 59–76, find the indicated root, or state that the expression is not a real number. ___ −⁴√256148views
Textbook QuestionIn Exercises 59–72, simplify each expression using the products-to-powers rule. (-2x⁻⁵y⁴z²)⁻⁴155views
Textbook QuestionIn Exercises 55–78, use properties of rational exponents to simplify each expression. Assume that all variables represent positive numbers. (25x⁴y⁶)^½244views
Textbook QuestionSimplify each radical. Assume all variables represent positive real numbers. √192459views
Textbook QuestionIn Exercises 59–76, find the indicated root, or state that the expression is not a real number. __ ⁶√64168views
Textbook QuestionIn Exercises 55–78, use properties of rational exponents to simplify each expression. Assume that all variables represent positive numbers. (x^½y^-⅗)^½158views
Textbook QuestionIn Exercises 73–84, simplify each expression using the quotients-to-powers rule. (2/x)⁴145views
Textbook QuestionSimplify the radical expressions in Exercises 67–74, if possible. ⁵√64x^6/⁵√2x480views
Textbook QuestionIn Exercises 65–74, simplify each radical expression and then rationalize the denominator. 15 ------------ ³√-27x⁴y¹¹154views
Textbook QuestionSimplify each radical. Assume all variables represent positive real numbers. ∛250266views
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 3^¼156views
Textbook QuestionIn Exercises 73–84, simplify each expression using the quotients-to-powers rule. (x³/5)²189views
Textbook QuestionSimplify each radical. Assume all variables represent positive real numbers. - ∜243994views
Textbook QuestionIn Exercises 75–92, rationalize each denominator. Simplify, if possible. 15 ---------- √6 + 1164views
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^1/12286views
Textbook QuestionIn Exercises 73–84, simplify each expression using the quotients-to-powers rule. (- 3x/y)⁴156views
Textbook QuestionIn Exercises 77–90, simplify each expression. Include absolute value bars where necessary. __ ³√x³157views
Textbook QuestionSimplify each radical. Assume all variables represent positive real numbers. -9 ⁵√243274views
Textbook QuestionIn Exercises 75–92, rationalize each denominator. Simplify, if possible. 17 ---------- √10 - 2150views
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√x²162views
Textbook QuestionIn Exercises 77–90, simplify each expression. Include absolute value bars where necessary. __ ⁴√y⁴169views
Textbook QuestionIn Exercises 75–82, add or subtract terms whenever possible. ³√54xy^3−y³√128x268views
Textbook QuestionIn Exercises 75–92, rationalize each denominator. Simplify, if possible. 12 ------------ √7 + √3150views
Textbook QuestionSimplify each radical. Assume all variables represent positive real numbers. ∛(16 (-2)⁴ (2)⁸)301views
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. -8/27251views
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√8a⁶169views
Textbook QuestionIn Exercises 77–90, simplify each expression. Include absolute value bars where necessary. ____ ³√−8x³156views
Textbook QuestionIn Exercises 75–92, rationalize each denominator. Simplify, if possible. √b ---------- √a - √b138views
Textbook QuestionSimplify each expression. Write answers without negative exponents. Assume all vari-ables represent positive real numbers. See Examples 8 and 9. 8^2/3429views
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√x¹⁰y¹⁵153views
Textbook QuestionIn Exercises 77–90, simplify each expression. Include absolute value bars where necessary. ____ ³√(−5)³161views
Textbook QuestionSimplify each radical. Assume all variables represent positive real numbers. √24m⁶n⁵265views
Textbook QuestionSimplify each radical. Assume all variables represent positive real numbers. ∜(x⁴ + y⁴)278views
Textbook QuestionSimplify each radical. Assume all variables represent positive real numbers. ∛(27 + a³)232views
Textbook QuestionSimplify each radical. Assume all variables represent positive real numbers. ⁹√5³259views
Textbook QuestionSimplify each radical. Assume all variables represent positive real numbers. ⁶√11³232views
Textbook QuestionIn Exercises 83–90, evaluate each expression without using a calculator. 16^(−6/2)302views
Textbook QuestionSimplify each radical. Assume all variables represent positive real numbers. ⁸√5⁴291views
Textbook QuestionIn Exercises 75–92, rationalize each denominator. Simplify, if possible. 2√6 + √5 -------------- 3√6 - √5139views
Textbook QuestionSimplify each radical. Assume all variables represent positive real numbers. ⁶√x¹⁸y²686views
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)441views
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√x⁶y³155views
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)275views
Textbook QuestionIn Exercises 93–104, rationalize each numerator. Simplify, if possible. 5 √ --- 3179views
Textbook QuestionSimplify each radical. Assume all variables represent positive real numbers. ⁹√∜7³243views
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)248views
Textbook QuestionPerform the indicated operations. Assume all variables represent positive real numbers. 8√(2x) - √(8x) + √(72x)686views
Textbook QuestionIn Exercises 93–104, rationalize each numerator. Simplify, if possible. ³√2x ³√y153views
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)302views
Textbook QuestionPerform the indicated operations. Assume all variables represent positive real numbers. 3√72m² - 5√32m² - 3√18m²227views
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√ab153views
Textbook QuestionIn Exercises 85–116, simplify each exponential expression. (-¼x⁻⁴y⁵z⁻¹)(-12x⁻³y⁻¹z⁴)156views
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)303views
Textbook QuestionIn Exercises 93–104, rationalize each numerator. Simplify, if possible. √x + 4 √x162views
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^2385views
Textbook QuestionPerform the indicated operations. Assume all variables represent positive real numbers. 2∛3 + 4∛24 - ∛81237views
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√x174views
Textbook QuestionIn Exercises 93–104, rationalize each numerator. Simplify, if possible. √a - √b √a + √b221views
Textbook QuestionPerform the indicated operations. Assume all variables represent positive real numbers. ∜32 + 3∜2230views
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√y160views
Textbook QuestionPerform the indicated operations. Assume all variables represent positive real numbers. 2∛16 + ∛54223views
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√√x155views
Textbook QuestionIn Exercises 103–110, insert either <, >, or = in the shaded area to make a true statement. |−20| □ |−50|272views
Textbook QuestionPerform the indicated operations. Assume all variables represent positive real numbers. 3x∛xy² - 2∛8x⁴y²239views
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. ____ √√x²y158views
Textbook QuestionIn Exercises 85–116, simplify each exponential expression. -24a³b⁻⁵c⁵/-3a⁻⁶b⁻⁴c⁻⁷160views
Textbook QuestionIn Exercises 105–110, use an associative property to write an algebraic expression equivalent to each expression and simplify. 4+(6+x)155views
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)^3334views
Textbook QuestionIn Exercises 103–110, insert either <, >, or = in the shaded area to make a true statement. 30/40−3/4 □ 14/15⋅15/14304views
Textbook QuestionIn Exercises 107–114, simplify each exponential expression. Assume that variables represent nonzero real numbers. (x^−2 y)^−3/(x^2 y^−1)^3335views
Textbook QuestionIn Exercises 101–108, simplify by reducing the index of the radical. ⁹√x^6 y^3305views
Textbook QuestionIn Exercises 101–108, simplify by reducing the index of the radical. ¹²√x^4y^8297views
Textbook QuestionPerform the indicated operations. Assume all variables represent positive real numbers. ∛64xy² + ∛27x⁴y⁵239views
Textbook QuestionIn Exercises 107–114, simplify each exponential expression. Assume that variables represent nonzero real numbers. (3x−4 y z−7)(3x)−3275views
Textbook QuestionIn Exercises 111–114, simplify each expression. Assume that all variables represent positive numbers. (49x^−2y^4)^−1/2(xy^1/2)333views
Textbook QuestionPerform the indicated operations. Assume all variables represent positive real numbers. ∜81x⁶y³ - ∜16x¹⁰y³245views
Textbook QuestionIn Exercises 111–114, simplify each expression. Assume that all variables represent positive numbers. (x^−5/4y^1/3x^−3/4)^−6598views
Textbook QuestionPerform the indicated operations. Assume all variables represent positive real numbers. 5√6 + 2√10292views
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)^2265views
Textbook QuestionPerform the indicated operations. Assume all variables represent positive real numbers. √6(3 + √7)274views
Textbook QuestionIn Exercises 85–116, simplify each exponential expression. (20a⁻³b⁴c⁵/-2a⁻⁵b⁻²c)⁻²147views
Textbook QuestionPerform the indicated operations. Assume all variables represent positive real numbers. 4√3(√7 - 2√11)259views
Textbook QuestionIn Exercises 117–124, simplify each exponential expression. 9y⁴/x⁻² + (x⁻¹/y²)⁻²165views
Textbook QuestionPerform the indicated operations. Assume all variables represent positive real numbers. (√2 + 3) (√2 - 3)214views
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.161views
Textbook QuestionIn Exercises 117–124, simplify each exponential expression. (3x⁴/y⁻⁴)⁻¹(2x/y²)³171views
Textbook QuestionPerform the indicated operations. Assume all variables represent positive real numbers. (∛11 - 1) (∛11² + ∛11 +1)251views
Textbook QuestionIn Exercises 117–124, simplify each exponential expression. (-4x³y⁻⁵)⁻²(2x⁻⁸y⁻⁵)166views
Textbook QuestionIn Exercises 117–124, simplify each exponential expression. (2x²y⁴)⁻¹(4xy³)⁻³ / (x²y)⁻⁵(x³y²)⁴215views
Textbook QuestionPerform the indicated operations. Assume all variables represent positive real numbers. (3√2 + √3) (2√3 - √2)223views
Textbook QuestionPerform the indicated operations and/or simplify each expression. Assume all variables represent positive real numbers. 5/√2225views
Textbook QuestionPerform the indicated operations and/or simplify each expression. Assume all variables represent positive real numbers. ∛2/3279views
Textbook QuestionPerform the indicated operations and/or simplify each expression. Assume all variables represent positive real numbers. ∜2/25233views
Textbook QuestionPerform the indicated operations and/or simplify each expression. Assume all variables represent positive real numbers. √2/3x274views
Textbook QuestionPerform the indicated operations and/or simplify each expression. Assume all variables represent positive real numbers. √(x⁵y³)/z²300views
Textbook QuestionPerform the indicated operations and/or simplify each expression. Assume all variables represent positive real numbers. ∛8/x⁴241views
Textbook QuestionPerform the indicated operations and/or simplify each expression. Assume all variables represent positive real numbers. (∛mn • ∛m²) / ∛n²227views
Textbook QuestionPerform the indicated operations and/or simplify each expression. Assume all variables represent positive real numbers. (-4 /∛3 ) + (1/∛24) - ( 2/∛81)227views
Textbook QuestionPerform the indicated operations and/or simplify each expression. Assume all variables represent positive real numbers. ( 5/∛2) - ( 2/∛16) + (1/∛54)287views
Textbook QuestionRationalize each denominator. Assume all variables represent nonnegative numbers and that no denominators are 0. 1/(2 + √5)285views
Textbook QuestionRationalize each denominator. Assume all variables represent nonnegative numbers and that no denominators are 0. (√7 - 1) / (2√7 + 4√2)338views
Textbook QuestionRationalize each denominator. Assume all variables represent nonnegative numbers and that no denominators are 0. (p - 4) / (√p + 2)348views
Textbook QuestionRationalize each denominator. Assume all variables represent nonnegative numbers and that no denominators are 0. 3m / 2 + (√m + n)177views
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.332views