1) When raising a number to the 0 power, the result is 1. Negative exponents can be made positive by moving them to the denominator. 2) To multiply powers of the same base, add the exponents. For example, 2x3 * 4x4 = 8x7. 3) To divide powers of the same base, subtract the exponents. For example, x5/x3 = x2.

1. EXPONENT
PROPERTIES

2. 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

3. Examples: Simplify
1) 3-4 = 1
34
2) (-5)0 = 1
3) 3ab-2 =
3𝑎
𝑏2
4) =
5
𝑥6 𝑦
y
x5
6

4. 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

5. Simplify
5) a • a5 = a6
6) n2 • 2n3 • 7n = 14n6
7) 3x2 ·4y5·2x5 = 24x7y5

6. Distributing a Power
Raising a Power to a Power
(am)n = am•n
Raising a Product to a Power
(ab)m = am • bm

7. Simplify
8) (a4)7 = a 28
9)(4g5)2 = 16x10

8. 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

9. Examples
Simplify.
10) =
1
𝑏5
11) =
1𝑥6
2
b
b9
4
x
x
10
5 4
10