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Standardized Test Practice

3. Raise each side to the power. 2. ANSWER. The correct answer is D. 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. 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 ANSWER The correct answer is D. 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.

  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. 2 3 Raise each side to the power . for Examples 3 and 4 GUIDED PRACTICE Solve the equation. Check your solution. 5. 3x3/2 = 375 3x3/2 = 375 Write original equation. x3/2 = 125 Divide each side by 3. (x3/2)2/3= (125)2/3 x = 25 Simplify.

  5. 4 3 Raise each side to the power . for Examples 3 and 4 GUIDED PRACTICE Solve the equation. Check your solution. 6. –2x3/4 = –16 –2x3/4 = –16 Write original equation. x3/4 = 8 Divide each side by –2. (x3/4)4/3= 84/3 x= (81/3)4 Apply properties of exponent. Simplify. x = 16

  6. 7. = –2 = –2 x1/5 x1/5 – – 2 2 3 3 for Examples 3 and 4 GUIDED PRACTICE Solve the equation. Check your solution. Write original equation. x1/5= 3 Divide each side by –2/3. Raise each side to the power 5. (x1/5 )5= 35 x = 243 Simplify.

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

  8. for Examples 3 and 4 GUIDED PRACTICE 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.

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

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