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EXPONENT
PROPERTIES
Zero and Negatives
• Anything to the zero power is 1.
(xy)0 = 1
• Negative Exponents are not allowed in final answers. Move them to
the denominator to make positive.
3𝑥−2
=
3
𝑥2
Examples: Simplify
1) 3-4
2) (-5)0
3) 3ab-2
4)
1
34
1
3𝑎
𝑏2
5
𝑥6 𝑦
y
x5
6
Multiplying Powers of the Same Base
am • an = am+n
Hint: multiply the big numbers (coefficients), add the small numbers (exponents)
Example) 2x3 * 4x4 =8x7
Simplify
10) a • a5
11) n2 • 2n3 • 7n
12) 6y2 • 3y3 • 2y-7
13) a • b • a5
14) 3x2 ·4y5·2x5
5
4
7
6
3
2
6
1
44 aa
dd


14)
15)
Distributing a Power
Raising a Power to a Power
(am)n = am•n (e3)4
Raising a Product to a Power
(ab)m = am • bm
(2x3)4
Simplify
16) (a4)7
17) (a4)2 • (a2)5
18)(4g5)-2
19)(3p0)4·(p2h5k)3
Dividing
𝑥 𝑎
𝑥 𝑏
= 𝑥 𝑎−𝑏
• To divide, subtract exponents. Place remaining bases on
the side with the largest degree
Example)
𝑥5
𝑥3 =
𝑥2
1
𝑥3
𝑥5
=
1
𝑥2
Examples
Simplify. 23)
20)
21)
22) 24
b
b9
4
x
x4
10
ba
ba 34
3
2
2
zyx
zyx
34
412
15
25


yx
yx
83
25
4
20
All together now…

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