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Standardized Test Practice

3. Raise each side to the power. 2. EXAMPLE 3. Standardized Test Practice. SOLUTION. 4 x 2/3 = 36. Write original equation. x 2/3 = 9. Divide each side by 4. ( x 2/3 ) 3/2 = 9 3/2. x = 27. Simplify. ANSWER. The correct answer is D. 4/3. ( x + 2) 3/4. = 8 4/3.

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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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