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**Standardized Test Practice**

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 Raise each side to the power . 3 2 x = ±27 Simplify. The correct answer is D. ANSWER

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**Solve an equation with a rational exponent**

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)3/4 4/3 = 8 4/3 Raise each side to the power . 4 3 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.

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

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**Solve the equation. Check your solution.**

GUIDED PRACTICE for Examples 3 and 4 Solve the equation. Check your solution. x3/2 = 375 3x3/2 = 375 Write original equation. x3/2 = 125 Divide each side by 3. Raise each side to the power . 2 3 (x3/2)2/3 = (125)2/3 x = 25 Simplify.

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**Solve the equation. Check your solution.**

GUIDED PRACTICE for Examples 3 and 4 Solve the equation. Check your solution. 6. –2x3/4 = –16 –2x3/4 = –16 Write original equation. x3/4 = 8 Divide each side by –2. Raise each side to the power . 4 3 (x3/4)4/3 = 84/3 x = (81/3)4 Apply properties of exponent. x = 16 Simplify.

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**Solve the equation. Check your solution.**

GUIDED PRACTICE for Examples 3 and 4 Solve the equation. Check your solution. 2 3 x1/5 – = –2 7. 2 3 x1/5 – = –2 Write original equation. x1/5= 3 Divide each side by –2/3. (x1/5 )5= 35 Raise each side to the power 5. x = 243 Simplify.

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**Solve the equation. Check your solution.**

GUIDED PRACTICE for Examples 3 and 4 Solve the equation. Check your solution. 8. (x + 3)5/2 = 32 (x + 3)5/2 = 32 Write original equation. [(x+ 3)5/2]2/5 = 322/5 Raise each side to the power 2/5. x + 3 = (32• )2 5 1 Apply properties of exponent. x + 3 = 4 Simplify. x = 1 Simplify.

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**Solve the equation. Check your solution.**

GUIDED PRACTICE for Examples 3 and 4 Solve the equation. Check your solution. 9. (x – 5)4/3 = 81 (x – 5)4/3 = 81 Write original equation. [(x – 5)4/3]3/4 = (81)3/4 Raise each side to the power 3/4. x – 5 = (811/4)3 Apply properties of exponent. x – 5 = ±33 Simplify. x – 5 = ±27 Simplify. x – 5 = 27 or x – 5 = 27 Let (x – 5) equal 27 and –27. x = 32 or x = –22 Subtract 5 from both sides of each equation.

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**Solve the equation. Check your solution.**

GUIDED PRACTICE for Examples 3 and 4 Solve the equation. Check your solution. (x + 2)2/3 + 3 = 7 (x + 2)2/3 +3 = 7 Write original equation. (x + 2)2/3 = 4 Subtract each side by 3. [(x + 2)2/3]3/2 = 43/2 Raise each side to the power 3/2. x + 2 = (41/2)3 Apply properties of exponent. x +2 = 8 or x + 2 = 8 Simplify. x = 10 or 6 Simplify.

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