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Standardized Test Practice

This guide provides step-by-step instructions on how to solve equations with rational exponents. It includes detailed examples, such as solving (x + 2)^(3/4) - 1 = 7, and practices that reinforce your understanding. You'll learn how to apply properties of exponents, simplify equations, and check your solutions effectively. Also included are guided practice problems for reinforcement, making this a comprehensive resource for mastering rational exponents in equations. Ideal for students preparing for standardized tests or needing extra practice.

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Standardized Test Practice

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  1. 3 Raise each side to the power . 2 EXAMPLE 3 Standardized Test Practice SOLUTION 4x2/3 = 36 Write original equation. x2/3 = 9 Divide each side by 4. (x2/3)3/2= 93/2 x = 27 Simplify. ANSWER The correct answer is D.

  2. 4/3 (x + 2)3/4 = 8 4/3 Raise each side to the power . 4 3 EXAMPLE 4 Solve an equation with a rational exponent Solve (x + 2)3/4 – 1 = 7. (x + 2)3/4 – 1 = 7 Write original equation. (x + 2)3/4 = 8 Add 1 to each side. x + 2 = (8 1/3)4 Apply properties of exponents. x + 2 = 24 Simplify. x + 2 = 16 Simplify. x = 14 Subtract 2 from each side.

  3. ANSWER The solution is 14. Check this in the original equation. EXAMPLE 4 Solve an equation with a rational exponent

  4. 7. = –2 x1/5 – 2 3 for Examples 3 and 4 GUIDED PRACTICE Solve the equation. Check your solution. 8. (x + 3)5/2 = 32 5. 3x3/2 = 375 ANSWER x = 25 ANSWER x = 1 6. –2x3/4 = –16 9. (x – 5)5/3 = 243 x = 32 ANSWER x = 16 ANSWER 10. (x + 2)2/3 +3 = 7 x = 243 ANSWER ANSWER x = –10 or 6

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