Math 135
Rational Exponents
Solutions
Evaluate or simplify each expression. You should have no negative exponents in any
answers.
1
1. 625 4
Answer 1.
1
(54 ) 4 = 5
2
2. 64 3
Answer 2.
2
2
64 3 = (26 ) 3 = 24 = 16
2
3. 64− 3
Answer 3.
2 −1
2
1
64− 3 = (64) 3
= (16)−1 =
16
3
4. 49 2
Answer 4.
3
3
49 2 = (72 ) 2 = 73 = 343
3
5. 49− 2
Answer 5.
− 32
49
= 49
3
2
−1
= 343−1 =
1
343
1
6. 0.001 3
Answer 6.
1
0.001 3 = 10−3
31
= 10−1 =
1
10
4
7. 0.001− 3
Answer 7.
4
0.001− 3 = 10−3
University of Hawai‘i at Mānoa
45
− 43
= 104 = 10000
R Spring - 2014
Math 135
Rational Exponents
Solutions
5
8. (−8) 3
Answer 8.
5
(−8) 3 = (−2)3
35
= (−2)5 = −32
5
9. (−8)− 3
Answer 9.
5
5 −1
1
(−8)− 3 = (−8) 3
= (−32)−1 = −
32
2
4
10. (x2 + 1) 3 (x2 + 1) 3
Answer 10.
4
2
2
4
6
(x2 + 1) 3 (x2 + 1) 3 = (x2 + 1) 3 + 3 = (x2 + 1) 3 = (x2 + 1)2 = x4 + 2x2 + 1
3
11.
1
5
2z 2 x 3 y 3
1
4
1
6z 2 y − 3 x 3
Answer 11.
3
1
5
1
1 3 1 1 1 5 4
1
= z 2 − 2 x 3 − 3 y 3 + 3 = z 1 x0 y 3 = zy 3
3
3
3
x
2z 2 x 3 y 3
1
2
6z y
1
3
6
6
12.
− 43
1
(2x2 + 1)− 5 (2x2 + 1) 5 (x2 + 1)− 5
9
(x2 + 1) 5
Answer 12.
6
6
1
(2x2 + 1)− 5 (2x2 + 1) 5 (x2 + 1)− 5
(x2 + 1)
9
5
6
1
6
9
= (2x2 + 1)− 5 + 5 (x2 + 1)− 5 − 5
10
= (2x2 + 1)0 (x2 + 1)− 5
= (x2 + 1)−2
1
=
2
(x + 1)2
1
= 4
x + 2x2 + 1
University of Hawai‘i at Mānoa
46
R Spring - 2014