02:27Simplify Square Roots of Perfect Squares: Square Root of 81 & (121/144), Negative Square Root of 64Wendy685views
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√3171views
Textbook QuestionDetermine whether each statement is true or false. If false, correct the right side of the equation. (y^2)(y^5) = y^7245views
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 )^1/3332views
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 )^-1/3389views
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 )^-1/3239views
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 )^1/3298views
Textbook QuestionIn Exercises 1–20, use radical notation to rewrite each expression. Simplify, if possible. (-27)^⅓157views
Textbook QuestionIn Exercises 1–20, evaluate each expression, or state that the expression is not a real number. ___ -√ 36171views
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^1/3319views
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^1/3209views
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^-1/3237views
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=11173views
Textbook QuestionIn Exercises 1–20, use radical notation to rewrite each expression. Simplify, if possible. -16^¼176views
Textbook QuestionIn Exercises 1–20, evaluate each expression, or state that the expression is not a real number. ___ √-36171views
Textbook QuestionEvaluate each expression in Exercises 1–12, or indicate that the root is not a real number. √−25341views
Textbook QuestionIn Exercises 1–38, multiply as indicated. If possible, simplify any radical expressions that appear in the product. √6 (4√6 - 3√2)157views
Textbook QuestionIn Exercises 1–20, use radical notation to rewrite each expression. Simplify, if possible. (xy)^⅓154views
Textbook QuestionIn Exercises 1–20, evaluate each expression, or state that the expression is not a real number. ____ √1/25174views
Textbook QuestionPerform the operation and/or simplify each of the following. Assume all variables represent positive real numbers. √50250views
Textbook QuestionEvaluate each expression in Exercises 1–12, or indicate that the root is not a real number. √144+25283views
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^2/9271views
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)169views
Textbook QuestionIn Exercises 1–20, use radical notation to rewrite each expression. Simplify, if possible. (2xy³)^⅕244views
Textbook QuestionIn Exercises 1–20, evaluate each expression, or state that the expression is not a real number. ____ -√9/16168views
Textbook QuestionPerform the operation and/or simplify each of the following. Assume all variables represent positive real numbers. 3√xy - 8√xy213views
Textbook QuestionEvaluate each expression in Exercises 1–12, or indicate that the root is not a real number. √25−√16242views
Textbook QuestionPerform the operation and/or simplify each of the following. Assume all variables represent positive real numbers. (2 + √3) (2 - √3)238views
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√x199views
Textbook QuestionIn Exercises 1–20, use radical notation to rewrite each expression. Simplify, if possible. 81^3/2158views
Textbook QuestionIn Exercises 1–20, evaluate each expression, or state that the expression is not a real number. ____ √0.81180views
Textbook QuestionEvaluate each expression in Exercises 1–12, or indicate that the root is not a real number. √(−17)^2264views
Textbook QuestionIn Exercises 1–38, multiply as indicated. If possible, simplify any radical expressions that appear in the product. (7 + √2) (8 + √2)161views
Textbook QuestionIn Exercises 11–28, add or subtract as indicated. You will need to simplify terms to identify the like radicals. _ __ √5 + √20156views
Textbook QuestionIn Exercises 1–20, use the product rule to multiply. ___ _____ ⁶√x-5 ⋅ ⁶√(x-5)⁴174views
Textbook QuestionIn Exercises 1–38, multiply as indicated. If possible, simplify any radical expressions that appear in the product. (4 + √5) (10 - 3√5)168views
Textbook QuestionIn Exercises 11–28, add or subtract as indicated. You will need to simplify terms to identify the like radicals. __ __ 5√12 + √75144views
Textbook QuestionIn Exercises 1–38, solve each radical equation. _____ _____ √6x + 2 = √5x + 3162views
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)166views
Textbook QuestionIn Exercises 11–28, add or subtract as indicated. You will need to simplify terms to identify the like radicals. ___ ___ 5√45x - 2√20x158views
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⋅√ 8x300views
Textbook QuestionIn Exercises 11–28, add or subtract as indicated. You will need to simplify terms to identify the like radicals. __ __ 3³√24 + ³√81164views
Textbook QuestionIn Exercises 1–20, use radical notation to rewrite each expression. Simplify, if possible. (xy)^4/7228views
Textbook QuestionIn Exercises 1–20, evaluate each expression, or state that the expression is not a real number. ______ √16 − 25183views
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^2650views
Textbook QuestionIn Exercises 1–38, solve each radical equation. ____ ____ √x - 4 + √x + 4 = 4182views
Textbook QuestionIn Exercises 1–38, multiply as indicated. If possible, simplify any radical expressions that appear in the product. (√2 + √7)²162views
Textbook QuestionSimplify each expression. Assume all variables represent nonzero real numbers. See Examples 1–3. (6^4)^3242views
Textbook QuestionIn Exercises 25–34, use the zero-exponent rule to simplify each expression. 6⁰178views
Textbook QuestionIn Exercises 21–38, rewrite each expression with rational exponents. ___ ⁵√11x307views
Textbook QuestionIn Exercises 1–38, multiply as indicated. If possible, simplify any radical expressions that appear in the product. (√2x - √y)²158views
Textbook QuestionSimplify each expression. Assume all variables represent nonzero real numbers. See Examples 1–3. (-2x^5)^5245views
Textbook QuestionIn Exercises 11–28, add or subtract as indicated. You will need to simplify terms to identify the like radicals. ______ ___ √4x - 12 + √x-3141views
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^2/3640views
Textbook QuestionIn Exercises 1–38, multiply as indicated. If possible, simplify any radical expressions that appear in the product. (√6 + √2) (√6 - √2)161views
Textbook QuestionSimplify each expression. Assume all variables represent nonzero real numbers. See Examples 1–3. -(2x^0y^4)^3239views
Textbook QuestionIn Exercises 11–28, add or subtract as indicated. You will need to simplify terms to identify the like radicals. ___ ___ 4³√x⁴y² + 5x³√xy²163views
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^5/4382views
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)154views
Textbook QuestionSimplify each expression. Assume all variables represent nonzero real numbers. See Examples 1–3. (p^4/q)^2340views
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)^4/7435views
Textbook QuestionUse the quotient rule to simplify the expressions in Exercises 23–32. Assume that x > 0. √24x^4/√3x582views
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√ k²322views
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)156views
Textbook QuestionSimplify each expression. Assume all variables represent nonzero real numbers. See Examples 1–3. (-5n^4/r^2)^3713views
Textbook QuestionUse the quotient rule to simplify the expressions in Exercises 23–32. Assume that x > 0. √500x^3/√10x^−1277views
Textbook QuestionSimplify each expression. Assume all variables represent nonzero real numbers. See Examples 1–3. -(x^3y^5/z)^0673views
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 √5p³389views
Textbook QuestionIn Exercises 25–34, use the zero-exponent rule to simplify each expression. (13y)⁰268views
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 √2y⁵228views
Textbook QuestionIn Exercises 1–38, solve each radical equation. ____ _____ √x + 2 + √3x + 7 = 1238views
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)²159views
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. -6316views
Textbook QuestionIn Exercises 35–52, write each expression with positive exponents only. Then simplify, if possible. 3⁻²161views
Textbook QuestionIn Exercises 21–38, rewrite each expression with rational exponents. ____ (⁶√7xy² ) ⁵167views
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)³172views
Textbook QuestionIn Exercises 35–52, write each expression with positive exponents only. Then simplify, if possible. (-5)⁻²160views
Textbook QuestionIn Exercises 21–38, rewrite each expression with rational exponents. __ 2x ³√y²168views
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. -5⁻²303views
Textbook QuestionIn Exercises 39–54, rewrite each expression with a positive rational exponent. Simplify, if possible. 49^-½173views
Textbook QuestionWrite each expression without negative exponents, and evaluate if possible. Assume all variables represent nonzero real numbers. See Example 4. -5^-4286views
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. __ √x⁵164views
Textbook QuestionIn Exercises 35–52, write each expression with positive exponents only. Then simplify, if possible. x²y⁻³160views
Textbook QuestionIn Exercises 39–54, rewrite each expression with a positive rational exponent. Simplify, if possible. 27^-⅓152views
Textbook QuestionWrite each expression without negative exponents, and evaluate if possible. Assume all variables represent nonzero real numbers. See Example 4. (1/3)^-2237views
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. ___ √x⁶y⁷153views
Textbook QuestionIn Exercises 39–54, rewrite each expression with a positive rational exponent. Simplify, if possible. 16^-¾171views
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)^-2502views
Textbook QuestionWrite each expression without negative exponents, and evaluate if possible. Assume all variables represent nonzero real numbers. See Example 4. 4x^-2252views
Textbook QuestionUse the rules for radicals to perform the indicated operations. Assume all variable expressions represent positive real numbers. √7 • √28232views
Textbook QuestionWrite each expression without negative exponents, and evaluate if possible. Assume all variables represent nonzero real numbers. See Example 4. -a^-3254views
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√x³y¹⁷z²190views
Textbook QuestionIn Exercises 35–52, write each expression with positive exponents only. Then simplify, if possible. x⁻²/y⁻⁵165views
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√32x⁹y¹⁷166views
Textbook QuestionIn Exercises 35–52, write each expression with positive exponents only. Then simplify, if possible. a⁻⁴b⁷/c⁻³190views
Textbook QuestionIn Exercises 39–54, rewrite each expression with a positive rational exponent. Simplify, if possible. (2xy)^-7/10198views
Textbook QuestionUse the rules for radicals to perform the indicated operations. Assume all variable expressions represent positive real numbers. ⁵√x² • ⁵√x³304views
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)⁴152views
Textbook QuestionIn Exercises 39–54, rewrite each expression with a positive rational exponent. Simplify, if possible. 5xz^-⅓167views
Textbook QuestionUse the rules for radicals to perform the indicated operations. Assume all variable expressions represent positive real numbers. ∜ m² • ∜ m²244views
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√y¹⁸201views
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^12240views
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)202views
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^-2221views
Textbook QuestionIn Exercises 55–78, use properties of rational exponents to simplify each expression. Assume that all variables represent positive numbers. 3^¾ ⋅ 3^¼168views
Textbook QuestionUse the rules for radicals to perform the indicated operations. Assume all variable expressions represent positive real numbers. √14 • √3pqr363views
Textbook QuestionEvaluate each expression in Exercises 55–66, or indicate that the root is not a real number. ³√8276views
Textbook QuestionIn Exercises 45–66, divide and, if possible, simplify. ______ √54a⁷b¹¹ √3a⁻⁴b⁻²158views
Textbook QuestionIn Exercises 55–58, find the indicated function values for each function. ____ g(x) = −³√8x−8; g(2), g(1), g(0)168views
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^-6245views
Textbook QuestionIn Exercises 55–78, use properties of rational exponents to simplify each expression. Assume that all variables represent positive numbers. 16^¾ 16^¼157views
Textbook QuestionUse the rules for radicals to perform the indicated operations. Assume all variable expressions represent positive real numbers. ∛ 7x • ∛ 2y237views
Textbook QuestionSimplify each exponential expression in Exercises 23–64. 10x^4 y^9/30x^12 y^−3277views
Textbook QuestionIn Exercises 59–72, simplify each expression using the products-to-powers rule. (4x)³153views
Textbook QuestionUse the rules for radicals to perform the indicated operations. Assume all variable expressions represent positive real numbers. √9/25280views
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^-3417views
Textbook QuestionIn Exercises 55–78, use properties of rational exponents to simplify each expression. Assume that all variables represent positive numbers. x^½ ⋅ x^⅓153views
Textbook QuestionEvaluate each expression in Exercises 55–66, or indicate that the root is not a real number. ⁴√−16265views
Textbook QuestionIn Exercises 45–66, divide and, if possible, simplify. ______ ³√250x⁵y³ ³√2x³174views
Textbook QuestionIn Exercises 55–78, use properties of rational exponents to simplify each expression. Assume that all variables represent positive numbers. x^⅘ x^⅕164views
Textbook QuestionUse the rules for radicals to perform the indicated operations. Assume all variable expressions represent positive real numbers. - ∛5/8212views
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)^2267views
Textbook QuestionIn Exercises 45–66, divide and, if possible, simplify. ______ ⁵√96x¹²y¹¹ ⁵√3x²y⁻²159views
Textbook QuestionSimplify the radical expressions in Exercises 58 - 62. ∜(32x^5)/∜(16x) (Assume that x > 0.)319views
Textbook QuestionUse the rules for radicals to perform the indicated operations. Assume all variable expressions represent positive real numbers. ∜m/n⁴327views
Textbook QuestionEvaluate each expression in Exercises 55–66, or indicate that the root is not a real number. ⁵√(−3)^5305views
Textbook QuestionSimplify each exponential expression in Exercises 23–64. (3a^−5 b^2/12a^3 b^−4)^0296views
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+3145views
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 ⋅ √10y162views
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^-4215views
Textbook QuestionIn Exercises 59–76, find the indicated root, or state that the expression is not a real number. ___ ⁴√−16158views
Textbook QuestionEvaluate each expression in Exercises 55–66, or indicate that the root is not a real number. ⁶√1/64337views
Textbook QuestionIn Exercises 65–74, simplify each radical expression and then rationalize the denominator. 25 --------- √5x²y153views
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^4475views
Textbook QuestionIn Exercises 59–76, find the indicated root, or state that the expression is not a real number. ___ ⁵√−1181views
Textbook QuestionIn Exercises 59–72, simplify each expression using the products-to-powers rule. (-3x⁻²)⁻³151views
Textbook QuestionUse the rules for radicals to perform the indicated operations. Assume all variable expressions represent positive real numbers. ∜∛2285views
Textbook QuestionIn Exercises 65–74, simplify each radical expression and then rationalize the denominator. 150a³ - √ ---------- b⁵162views
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 ⋅ √10xy²148views
Textbook QuestionUse the rules for radicals to perform the indicated operations. Assume all variable expressions represent positive real numbers. ⁵√∛9270views
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)^-2464views
Textbook QuestionIn Exercises 59–76, find the indicated root, or state that the expression is not a real number. ___ ⁶√−1159views
Textbook QuestionIn Exercises 59–72, simplify each expression using the products-to-powers rule. (5x³y⁻⁴)⁻²159views
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 √ ------------- 15m³n⁴159views
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√6160views
Textbook QuestionIn Exercises 59–76, find the indicated root, or state that the expression is not a real number. ___ −⁴√256150views
Textbook QuestionIn Exercises 59–72, simplify each expression using the products-to-powers rule. (-2x⁻⁵y⁴z²)⁻⁴156views
Textbook QuestionIn Exercises 55–78, use properties of rational exponents to simplify each expression. Assume that all variables represent positive numbers. (25x⁴y⁶)^½248views
Textbook QuestionSimplify each radical. Assume all variables represent positive real numbers. √192463views
Textbook QuestionIn Exercises 59–76, find the indicated root, or state that the expression is not a real number. __ ⁶√64174views
Textbook QuestionIn Exercises 55–78, use properties of rational exponents to simplify each expression. Assume that all variables represent positive numbers. (x^½y^-⅗)^½161views
Textbook QuestionIn Exercises 73–84, simplify each expression using the quotients-to-powers rule. (2/x)⁴146views
Textbook QuestionSimplify the radical expressions in Exercises 67–74, if possible. ⁵√64x^6/⁵√2x482views
Textbook QuestionIn Exercises 65–74, simplify each radical expression and then rationalize the denominator. 15 ------------ ³√-27x⁴y¹¹156views
Textbook QuestionSimplify each radical. Assume all variables represent positive real numbers. ∛250269views
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 3^¼157views
Textbook QuestionIn Exercises 73–84, simplify each expression using the quotients-to-powers rule. (x³/5)²191views
Textbook QuestionSimplify each radical. Assume all variables represent positive real numbers. - ∜2431005views
Textbook QuestionIn Exercises 75–92, rationalize each denominator. Simplify, if possible. 15 ---------- √6 + 1167views
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^1/12289views
Textbook QuestionIn Exercises 73–84, simplify each expression using the quotients-to-powers rule. (- 3x/y)⁴158views
Textbook QuestionIn Exercises 77–90, simplify each expression. Include absolute value bars where necessary. __ ³√x³160views
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 - 2152views
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√x²164views
Textbook QuestionIn Exercises 77–90, simplify each expression. Include absolute value bars where necessary. __ ⁴√y⁴171views
Textbook QuestionIn Exercises 75–82, add or subtract terms whenever possible. ³√54xy^3−y³√128x270views
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)302views
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. -8/27253views
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√8a⁶172views
Textbook QuestionIn Exercises 77–90, simplify each expression. Include absolute value bars where necessary. ____ ³√−8x³159views
Textbook QuestionIn Exercises 75–92, rationalize each denominator. Simplify, if possible. √b ---------- √a - √b141views
Textbook QuestionSimplify each expression. Write answers without negative exponents. Assume all vari-ables represent positive real numbers. See Examples 8 and 9. 8^2/3432views
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√x¹⁰y¹⁵155views
Textbook QuestionIn Exercises 77–90, simplify each expression. Include absolute value bars where necessary. ____ ³√(−5)³163views
Textbook QuestionSimplify each radical. Assume all variables represent positive real numbers. √24m⁶n⁵267views
Textbook QuestionSimplify each radical. Assume all variables represent positive real numbers. ∜(x⁴ + y⁴)280views
Textbook QuestionSimplify each radical. Assume all variables represent positive real numbers. ∛(27 + a³)234views
Textbook QuestionSimplify each radical. Assume all variables represent positive real numbers. ⁹√5³261views
Textbook QuestionSimplify each radical. Assume all variables represent positive real numbers. ⁶√11³238views
Textbook QuestionIn Exercises 83–90, evaluate each expression without using a calculator. 16^(−6/2)303views
Textbook QuestionSimplify each radical. Assume all variables represent positive real numbers. ⁸√5⁴293views
Textbook QuestionIn Exercises 75–92, rationalize each denominator. Simplify, if possible. 2√6 + √5 -------------- 3√6 - √5142views
Textbook QuestionSimplify each radical. Assume all variables represent positive real numbers. ⁶√x¹⁸y²690views
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)448views
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√x⁶y³160views
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)276views
Textbook QuestionIn Exercises 93–104, rationalize each numerator. Simplify, if possible. 5 √ --- 3182views
Textbook QuestionSimplify each radical. Assume all variables represent positive real numbers. ⁹√∜7³246views
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)249views
Textbook QuestionPerform the indicated operations. Assume all variables represent positive real numbers. 8√(2x) - √(8x) + √(72x)690views
Textbook QuestionIn Exercises 93–104, rationalize each numerator. Simplify, if possible. ³√2x ³√y155views
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)303views
Textbook QuestionPerform the indicated operations. Assume all variables represent positive real numbers. 3√72m² - 5√32m² - 3√18m²229views
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√ab156views
Textbook QuestionIn Exercises 85–116, simplify each exponential expression. (-¼x⁻⁴y⁵z⁻¹)(-12x⁻³y⁻¹z⁴)160views
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)304views
Textbook QuestionIn Exercises 93–104, rationalize each numerator. Simplify, if possible. √x + 4 √x164views
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^2388views
Textbook QuestionPerform the indicated operations. Assume all variables represent positive real numbers. 2∛3 + 4∛24 - ∛81239views
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√x176views
Textbook QuestionIn Exercises 93–104, rationalize each numerator. Simplify, if possible. √a - √b √a + √b223views
Textbook QuestionPerform the indicated operations. Assume all variables represent positive real numbers. ∜32 + 3∜2232views
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√y162views
Textbook QuestionPerform the indicated operations. Assume all variables represent positive real numbers. 2∛16 + ∛54226views
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√√x156views
Textbook QuestionIn Exercises 103–110, insert either <, >, or = in the shaded area to make a true statement. |−20| □ |−50|275views
Textbook QuestionPerform the indicated operations. Assume all variables represent positive real numbers. 3x∛xy² - 2∛8x⁴y²242views
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. ____ √√x²y159views
Textbook QuestionIn Exercises 85–116, simplify each exponential expression. -24a³b⁻⁵c⁵/-3a⁻⁶b⁻⁴c⁻⁷162views
Textbook QuestionIn Exercises 105–110, use an associative property to write an algebraic expression equivalent to each expression and simplify. 4+(6+x)157views
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)^3338views
Textbook QuestionIn Exercises 103–110, insert either <, >, or = in the shaded area to make a true statement. 30/40−3/4 □ 14/15⋅15/14307views
Textbook QuestionIn Exercises 107–114, simplify each exponential expression. Assume that variables represent nonzero real numbers. (x^−2 y)^−3/(x^2 y^−1)^3338views
Textbook QuestionIn Exercises 101–108, simplify by reducing the index of the radical. ⁹√x^6 y^3306views
Textbook QuestionIn Exercises 101–108, simplify by reducing the index of the radical. ¹²√x^4y^8298views
Textbook QuestionPerform the indicated operations. Assume all variables represent positive real numbers. ∛64xy² + ∛27x⁴y⁵241views
Textbook QuestionIn Exercises 107–114, simplify each exponential expression. Assume that variables represent nonzero real numbers. (3x−4 y z−7)(3x)−3277views
Textbook QuestionIn Exercises 111–114, simplify each expression. Assume that all variables represent positive numbers. (49x^−2y^4)^−1/2(xy^1/2)335views
Textbook QuestionPerform the indicated operations. Assume all variables represent positive real numbers. ∜81x⁶y³ - ∜16x¹⁰y³247views
Textbook QuestionIn Exercises 111–114, simplify each expression. Assume that all variables represent positive numbers. (x^−5/4y^1/3x^−3/4)^−6601views
Textbook QuestionPerform the indicated operations. Assume all variables represent positive real numbers. 5√6 + 2√10296views
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)^2267views
Textbook QuestionPerform the indicated operations. Assume all variables represent positive real numbers. √6(3 + √7)275views
Textbook QuestionIn Exercises 85–116, simplify each exponential expression. (20a⁻³b⁴c⁵/-2a⁻⁵b⁻²c)⁻²151views
Textbook QuestionPerform the indicated operations. Assume all variables represent positive real numbers. 4√3(√7 - 2√11)261views
Textbook QuestionIn Exercises 117–124, simplify each exponential expression. 9y⁴/x⁻² + (x⁻¹/y²)⁻²169views
Textbook QuestionPerform the indicated operations. Assume all variables represent positive real numbers. (√2 + 3) (√2 - 3)217views
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.164views
Textbook QuestionIn Exercises 117–124, simplify each exponential expression. (3x⁴/y⁻⁴)⁻¹(2x/y²)³172views
Textbook QuestionPerform the indicated operations. Assume all variables represent positive real numbers. (∛11 - 1) (∛11² + ∛11 +1)253views
Textbook QuestionIn Exercises 117–124, simplify each exponential expression. (-4x³y⁻⁵)⁻²(2x⁻⁸y⁻⁵)168views
Textbook QuestionIn Exercises 117–124, simplify each exponential expression. (2x²y⁴)⁻¹(4xy³)⁻³ / (x²y)⁻⁵(x³y²)⁴219views
Textbook QuestionPerform the indicated operations. Assume all variables represent positive real numbers. (3√2 + √3) (2√3 - √2)230views
Textbook QuestionPerform the indicated operations and/or simplify each expression. Assume all variables represent positive real numbers. 5/√2227views
Textbook QuestionPerform the indicated operations and/or simplify each expression. Assume all variables represent positive real numbers. ∛2/3282views
Textbook QuestionPerform the indicated operations and/or simplify each expression. Assume all variables represent positive real numbers. ∜2/25239views
Textbook QuestionPerform the indicated operations and/or simplify each expression. Assume all variables represent positive real numbers. √2/3x276views
Textbook QuestionPerform the indicated operations and/or simplify each expression. Assume all variables represent positive real numbers. √(x⁵y³)/z²302views
Textbook QuestionPerform the indicated operations and/or simplify each expression. Assume all variables represent positive real numbers. ∛8/x⁴243views
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)229views
Textbook QuestionPerform the indicated operations and/or simplify each expression. Assume all variables represent positive real numbers. ( 5/∛2) - ( 2/∛16) + (1/∛54)289views
Textbook QuestionRationalize each denominator. Assume all variables represent nonnegative numbers and that no denominators are 0. 1/(2 + √5)288views
Textbook QuestionRationalize each denominator. Assume all variables represent nonnegative numbers and that no denominators are 0. (√7 - 1) / (2√7 + 4√2)340views
Textbook QuestionRationalize each denominator. Assume all variables represent nonnegative numbers and that no denominators are 0. (p - 4) / (√p + 2)351views
Textbook QuestionRationalize each denominator. Assume all variables represent nonnegative numbers and that no denominators are 0. 3m / 2 + (√m + n)179views
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.340views