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Standardized Test PracticeEXAMPLE 3
SOLUTION
4x2/3 = 36 Write original equation.
x2/3 = 9 Divide each side by 4.
(x2/3)3/2 = 93/2
x = ±27 Simplify.
Raise each side to the power .32
The correct answer is D.
ANSWER
Solve an equation with a rational exponentEXAMPLE 4
Solve (x + 2)3/4 – 1 = 7.
(x + 2)3/4 – 1 = 7
(x + 2)3/4 = 8
(x + 2)3/4 4/3= 8 4/3
x + 2 = (8 1/3)4
x + 2 = 24
x + 2 = 16
Write original equation.
Add 1 to each side.
Simplify.
Apply properties of exponents.
Raise each side to the power .43
Simplify.
x = 14 Subtract 2 from each side.
Solve an equation with a rational exponent
EXAMPLE 4
The solution is 14. Check this in the original equation.
ANSWER
GUIDED PRACTICE for Examples 3 and 4
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 Raise each side to the power .2
3
x = 25 Simplify.
GUIDED PRACTICE for Examples 3 and 4
Solve the equation. Check your solution.
6. –2x3/4 = –16
Write original equation.
x3/4 = 8 Divide each side by –2.
(x3/4)4/3 = 84/3 Raise each side to the power .4
3
Simplify.
x = (81/3)4 Apply properties of exponent.
x = 16
–2x3/4 = –16
GUIDED PRACTICE for Examples 3 and 4
Solve the equation. Check your solution.
23
x1/5 – = –27.
Write original equation.
(x1/5 )5= 35
Divide each side by –2/3.
x = 243
Raise each side to the power 5.
Simplify.
23
x1/5 – = –2
x1/5= 3
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.
Apply properties of exponent. x + 3 = (32• )2
51
x + 3 = 4
x = 1 Simplify.
Simplify.
GUIDED PRACTICE for Examples 3 and 4
Solve the equation. Check your solution.
9. (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.
Apply properties of exponent. x – 5 = (811/4)3
x – 5 = ±33
x – 5 = ±27 Simplify.
Simplify.
(x – 5)4/3 = 81
x – 5 = 27 or x – 5 = 27
x = 32 or x = –22
Let (x – 5) equal 27 and –27.
Subtract 5 from both sides of each equation.
GUIDED PRACTICE for Examples 3 and 4
Solve the equation. Check your solution.
10. (x + 2)2/3 + 3 = 7
Write original equation.
(x + 2)2/3 = 4
Raise each side to the power 3/2.
Apply properties of exponent.
x +2 = 8 or x + 2 = 8
Simplify.
Simplify.
(x + 2)2/3 +3 = 7
[(x + 2)2/3]3/2 = 43/2
x + 2 = (41/2)3
x = 10 or 6
Subtract each side by 3.
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