0. Review of Algebra

In Exercises 1–14, multiply using the product rule. b⁴•b⁷

Write ∛64 using exponents and evaluate.

In this Exercise Set, assume that all variables represent positive real numbers. In Exercises 1–10, add or subtract as indicated. _ _ 7√3 + 2√3

Determine whether each statement is true or false. If false, correct the right side of the equation. (y^2)(y^5) = y^7

Write 27^2/3 in radical form and evaluate.

In Exercises 1–14, multiply using the product rule. x•x³

Match the rational exponent expression in Column I with the equivalent radical expression in Column II. Assume that x is not 0. (c) ( 3x )^1/3

Evaluate each exponential expression in Exercises 1–22. (−2)^6

Match the rational exponent expression in Column I with the equivalent radical expression in Column II. Assume that x is not 0. (d) ( 3x )^-1/3

Match the rational exponent expression in Column I with the equivalent radical expression in Column II. Assume that x is not 0. (b) ( -3x )^-1/3

Match the rational exponent expression in Column I with the equivalent radical expression in Column II. Assume that x is not 0. (a) ( -3x )^1/3

In Exercises 1–20, use radical notation to rewrite each expression. Simplify, if possible. (-27)^⅓

In Exercises 1–20, evaluate each expression, or state that the expression is not a real number. ___ -√ 36

Match the rational exponent expression in Column I with the equivalent radical expression in Column II. Assume that x is not 0. (a) -3x^1/3

Match the rational exponent expression in Column I with the equivalent radical expression in Column II. Assume that x is not 0. (d) 3x^1/3

Match the rational exponent expression in Column I with the equivalent radical expression in Column II. Assume that x is not 0. (c) 3x^-1/3

In Exercises 4–6, evaluate each algebraic expression for the given value or values of the variable. 6+2(x-8)³, for x=11

In Exercises 1–20, use radical notation to rewrite each expression. Simplify, if possible. -16^¼

In Exercises 1–20, evaluate each expression, or state that the expression is not a real number. ___ √-36

Evaluate each expression in Exercises 1–12, or indicate that the root is not a real number. √−25

In Exercises 1–38, multiply as indicated. If possible, simplify any radical expressions that appear in the product. √6 (4√6 - 3√2)

In Exercises 1–20, use the product rule to multiply. _ _ ⁴√9 ⋅ ⁴√3

In Exercises 1–20, use radical notation to rewrite each expression. Simplify, if possible. (xy)^⅓

In Exercises 1–20, evaluate each expression, or state that the expression is not a real number. ____ √1/25

Perform the operation and/or simplify each of the following. Assume all variables represent positive real numbers. √50

Evaluate each expression in Exercises 1–12, or indicate that the root is not a real number. √144+25

In Exercises 1–20, use the product rule to multiply. __ ___ √5x ⋅ √11y

Determine whether each statement is true or false. If false, correct the right side of the equation. (m^2/3)(m^1/3) = m^2/9

In Exercises 1–38, solve each radical equation. _____ x = √6x + 7

In Exercises 1–38, multiply as indicated. If possible, simplify any radical expressions that appear in the product. ³√3 (³√6 + 7 ³√4)

In Exercises 1–20, use radical notation to rewrite each expression. Simplify, if possible. (2xy³)^⅕

In Exercises 1–20, evaluate each expression, or state that the expression is not a real number. ____ -√9/16

Perform the operation and/or simplify each of the following. Assume all variables represent positive real numbers. 3√xy - 8√xy

Evaluate each expression in Exercises 1–12, or indicate that the root is not a real number. √25−√16

Perform the operation and/or simplify each of the following. Assume all variables represent positive real numbers. (2 + √3) (2 - √3)

In Exercises 1–20, use the product rule to multiply. ___ __ ⁴√6x² ⋅ ⁴√3x

Match 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. -1/125

In Exercises 1–38, solve each radical equation. _____ √2x + 1 = x - 7

In Exercises 1–38, multiply as indicated. If possible, simplify any radical expressions that appear in the product. ³√x (³√24x² - ³√x)

Rewrite each expression without the absolute value bars. |√2-1|

In 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√x

In Exercises 1–20, use radical notation to rewrite each expression. Simplify, if possible. 81^3/2

In Exercises 1–20, evaluate each expression, or state that the expression is not a real number. ____ √0.81

Write each root using exponents and evaluate. ∛125

Evaluate each exponential expression in Exercises 1–22. 4^−3

In Exercises 1–14, multiply using the product rule. (5x³y⁴)(20x⁷y⁸)

Write each root using exponents and evaluate. ∛216

Evaluate each expression in Exercises 1–12, or indicate that the root is not a real number. √(−17)^2

In Exercises 1–20, use the product rule to multiply. ___ ___ √x+6 ⋅ √x-6

Simplify each expression. See Example 1. (3y^4)(-6y^3)

In Exercises 1–38, solve each radical equation. _____ x = √3x + 7 - 3

In Exercises 1–38, multiply as indicated. If possible, simplify any radical expressions that appear in the product. (7 + √2) (8 + √2)

In Exercises 11–28, add or subtract as indicated. You will need to simplify terms to identify the like radicals. _ __ √5 + √20

Simplify each expression. See Example 1. (n^6)(n^4)(n)

Evaluate each exponential expression in Exercises 1–22. 2^2⋅2^3

In Exercises 1–14, multiply using the product rule. (-3x⁴y⁰z)(-7xyz³)

Simplify each expression. See Example 1. (a^8)(a^5)(a)

In Exercises 1–20, use the product rule to multiply. ___ _____ ⁶√x-5 ⋅ ⁶√(x-5)⁴

In Exercises 1–38, solve each radical equation. _____ 3x - √3x + 7 = -5

In Exercises 1–38, multiply as indicated. If possible, simplify any radical expressions that appear in the product. (4 + √5) (10 - 3√5)

In Exercises 11–28, add or subtract as indicated. You will need to simplify terms to identify the like radicals. __ __ 5√12 + √75

Write each root using exponents and evaluate. ∜256

Write each root using exponents and evaluate. ∛-125

In Exercises 1–38, solve each radical equation. _____ _____ √6x + 2 = √5x + 3

In Exercises 1–38, multiply as indicated. If possible, simplify any radical expressions that appear in the product. (7 - 2√7) (5 - 3√7)

In Exercises 11–28, add or subtract as indicated. You will need to simplify terms to identify the like radicals. ___ ___ 5√45x - 2√20x

Evaluate each exponential expression in Exercises 1–22. (3^3)^2

Write each root using exponents and evaluate. ∛-343

Write each root using exponents and evaluate. ∜-81

In Exercises 15–24, divide using the quotient rule. 15x⁹/3x⁴

Use the product rule to simplify the expressions in Exercises 13–22. In Exercises 17–22, assume that variables represent nonnegative real numbers. √10x⋅√ 8x

In Exercises 11–28, add or subtract as indicated. You will need to simplify terms to identify the like radicals. __ __ 3³√24 + ³√81

Write each root using exponents and evaluate. ∜-256

Evaluate each exponential expression in Exercises 1–22. 3^8/3^4

Write each root using exponents and evaluate. ⁵√32

In Exercises 15–24, divide using the quotient rule. x⁹y⁷/x⁴y²

Simplify each expression. See Example 1. (5x^2y)(-3x^3y^4)

In Exercises 1–20, use radical notation to rewrite each expression. Simplify, if possible. (xy)^4/7

In Exercises 1–20, evaluate each expression, or state that the expression is not a real number. ______ √16 − 25

Evaluate each exponential expression in Exercises 1–22. 2^3/2^7

In Exercises 15–24, divide using the quotient rule. 50x²y⁷/5xy⁴

In Exercises 21–38, rewrite each expression with rational exponents. _ √7

Write each root using exponents and evaluate. - ∛-343

Use the product rule to simplify the expressions in Exercises 13–22. In Exercises 17–22, assume that variables represent nonnegative real numbers. √6x⋅√3x^2

Simplify each expression. See Example 1. (35m^4n)(-2/7mn^2)

In Exercises 21–32, simplify by factoring. __ √27

Simplify each exponential expression in Exercises 23–64. x^−2y

In Exercises 15–24, divide using the quotient rule. -56a^12b^10c^8/7ab^2c^4

In Exercises 21–38, rewrite each expression with rational exponents. _ ∛5

In Exercises 21–32, simplify by factoring. __ √28

In Exercises 1–38, solve each radical equation. ____ ____ √x - 4 + √x + 4 = 4

In Exercises 1–38, multiply as indicated. If possible, simplify any radical expressions that appear in the product. (√2 + √7)²

Simplify each expression. Assume all variables represent nonzero real numbers. See Examples 1–3. (6^4)^3

In Exercises 25–34, use the zero-exponent rule to simplify each expression. 6⁰

In Exercises 21–38, rewrite each expression with rational exponents. ___ ⁵√11x

In Exercises 21–32, simplify by factoring. ___ √40x

In Exercises 1–38, solve each radical equation. ____ 2√x - 3 + 4 = x + 1

In Exercises 1–38, multiply as indicated. If possible, simplify any radical expressions that appear in the product. (√2x - √y)²