1. 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

2. 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.

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

4. 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.

5. 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.

6. 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.

7. 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.

8. 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.

9. 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.