Algebra 1
Exponent Practice #1
Name: ______________________________
Simplify each expression completely. Assume that no variable is equal to zero. Final
answers should include no negative exponents. You must copy the original problem. The
problems labeled with an asterisk (*), write out each factor individually and then simplify.
Set A: Product of Powers and Extension (Rules #1, 2)
*1.
*2.
3.
4.
5.
*6.
*7.
8.
9.
42 • 43
x2 • x4
y4 • y3
62 • 63
g5 • g6
f3 • f3
k4 • k3
w • w5
k2 • k3 • k2
*10.
11.
*12.
13.
14.
€ 15.
*16.
17.
18.
a5(a)(a3)
(b 8 )(b 6 )(b 20 )
(-10e4)(2e5)
33 • 32 • 3
x7 • x2
g15 • g
-5y2 • 2y
94 • 92
-3p6 • 5p9
19.
20.
21.
22.
*23.
24.
*25.
26.
h4 • h3 • h2
6r100 • -8r90
s14 • s9
4g171 • g75
-60d4 • -15d2 • 2
(-8y5)(5y)
(3a2)(4a3)
(-15e3)(-2e4)
Set B: Power of a Power and Power of a Product (Rules #3, 4)
*1.
2.
*3.
4.
5.
6.
*7.
*8.
(34)2
(72)6
(c4)3
(x3)4
(s2)2
(j5)3
(-m2)2
-(m2)2
*9.
*10.
11.
12.
*13.
*14.
*15.
16.
(3p)4
(6y)2
(10x)5
(22)4
(a 3 ) 4 (a 2 )
(6q)2(-1q)
(7x)2(5x)(2x)2
(-12r)(r)2(-2r)
12.
13.
*14.
15.
*16.
17.
18.
*19.
20.
*21.
22.
*23.
-3(2w)4
(-3b)6(2b5)
(4dkm)3
(4d1k1m1)3
(5x5)2(3x6)(3x2)2
(-4r3)(12r2)2(5r)
(r3•r4)3(r4•r4)2
(-11m4)(-6m3)3
(8d6)5(-6d2b5)8
(-4m7n9)3
(42x3y2)7
(p6)2(8p5n4)4
*17.
18.
*19.
20.
*21.
€ 22.
a5(a3)2(a5)3
(b 8 )4 (b 6 )2 (b 20 )3
(-10e)5(2e)3
(-8y)8(5y)4
(3a)2(4a)2
(-15e)5(-2e)2
€
Set C: Extension of Power of a Power and Power of a Product (Rule #5)
*1.
*2.
3.
*4.
*5.
*6.
€ 7.
8.
9.
*10.
11.
(3y3)4
(6y5)2
(2a 3 )4 (a 2 )
(3q2)3(2q4)
-(3xy)2
(-3xy)2
-2(xz)5
(-2xz)5
(8d6)7(-6d2)6
(p6)4(8p5)
(6y3)10(-4y2)7
24.
25.
26.
27.
28.
*29.
30.
31.
*32.
33.
(6x2y3)(-4x4y2)
-3(2wz)4
(-3ab)3(2b3)
(c3)5(d3)13
(r3t4)3(r4t4)5
(-11m4)(-6m3p2)2
(4a12b11)3
(2wz)40
(5x5)2(3y6)3(3x2)
(-4r3)10(12r-2)15(5r)
Set D: Quotient of Powers and Extension (Rules #6, 7)
*1.
*2.
€ *3.
€ 4.
€
*5.
€
6.
36n 5
12n
a 5b 6
ab 5
x2 y4
y2
z 33
z16
- 10b 6
− 2b 2
−4f 5
−4f 2
7.
*8.
€
€
*9.
10.
€ *11.
€ *12.
−12x 7
6x 2
4c 2 d 3
cd 3
2
( x 3 y 5 z)
4 2
x z
10s 7
5s 4
35z10
5z 8
10m 6 n 3
5m 2 n
€
Set E: Power of a Quotient and Extension (Rules #8, #9)
*1.
*2.
€
€
€
€
€
€
3.
4.
*5.
*6.
 2 2
 
5
 −x 3 4
 2 
 y 
 m 3
 4
n 
 (−t)2 8
 6 
 y 
12 3
 
17 
 −k 13 4
 11 
h 
€
7.
8.
€
€
€
€
*9.
*10.
11.
12.
 5 6
 4
j 
 m12 10
 7
− p 
 3x 2
 
 5x 
 7x 3 4

2
10y 
 5 2 m 3

5 4
 (−3) n 
 8t 2 8
 2 4
6 y 
€
Set F: Zero Exponents Property (Rule #10)
1.
2.
3.
4.
5
6.
7.
(c3)5(d3)0
(yz)0
(3a2b6)0
(60)4
(7m5n)2(-3mn3)0
(2x4)2(6x)0(-3x4)
c0
c −3
€
8.
9.
10.
11.
€ 12.
13.
 9a 6b−3  0

−8 
18a b 
(-12r0)(r)2(-2r)
(5x5)2(3x6)(3x2)0
(-4r3)(12r2)0(5r)
(r3•r0)3(r4•r4)0
(4a0b11)3
13.
14.
€ *15.
€ 16.
€ 17.
x11 y 3
x11 y
y14
y10
32 m 5 p 6
3 m2 p5
−8 p 34
2 p 23
d 2e4 f
de2
€
€
*13.
*14.
€
€
€
15.
16.
17.
 2 5 m 3

4
 −7k 
10 6 k 7 4
 12 
 3h 
 −5r 3 6
 2 4
3 s 
 9m 4 10
 7 3
6 p 
 −32 y 4 10
 17 3 
2 r 
€
€
14.
15.
16.
€ 17.
€
€
(2wz)0
x0 y4
y2
z 33
z0
35z 0
5z 8
Set G: Negative Exponents (Rule #11)
*1.
€
2.
3.
4.
*5.
6.
7.
8.
€ 9.
10.
*11.
12.
13.
€ 14.
15.
16.
17.
€ 18.
19.
20.
21.
22.
x2
x5
x-4
25-2
b-5
15m 4
5m 7
k-4
j-1
x-2y-2
a4z-4
f-3k5
28 p 2
4 p3
-2 -1
j k
p-1r-1
j 3k 2
4 j5k 3
5-2
4-2
2-3
10-1
1
x −3
25-1
23
3− 2
100-1
23.
24.
25.
*26.
27.
28.
29.
30.
31.
32.
*33.
34.
35.
*36.
37.
€
€
€
38.
0.5-2
0.25-1
(-2)-3
a 2b 3
a 3b 2
(6-2)-1
(5a)-3
(10x2y-3)-1
(-2m3)(3m-3)
1
x −4
− 11u 5 g 2
− 9u 3 g 4
− 4a 6 m 5
12a 2 m 6
16 x 5 y 2
2x3 y3
− 5v 4 r 3
− 10v 3 r 5
 c 3d 5 3
 6 
c d
 1 −2
 
 3
 3 −2
 2
x 
39.
 6x 2 z 3 −1
 4 
 3x z 
40.
 2a 5b 3 −2

6 
 5ab 
€ 41.
2
7
€ 42.
€
43.
€
44.
€
45.
3 2
2 −2 −1
(8a b ) (4ab )
(6y z) (2y z )
(−4 y z )
2 5 3
12 8 2
−15w 5 y −3 z 2
−3w 4 y −7 z 7
 2x −1 8x 4 
 3   −2 
 3y   9y 
2 5 −1
(−9b c ) (3b c )
4 5
€ 46.
 5w 6 y −3 z 4 −2

5 2 −1 
 20w y z 
€
(2a ) (−4a )
3 3
47.
€
€
€
48.
20a 6
 50c 3 d −1 −2

2 4 
 25c d 
2 2