1. Properties of Exponents
August 27th, 2013

2. Exponential Expressions in Expanded Form
Write Each Expression in expanded form
(4𝑦) 3
(4𝑦)(4𝑦)(4𝑦)
−𝑎 2
-(a ∙ a) = -𝑎∙𝑎
2 𝑦 2 ( 𝑥−3) 3
2 𝑦 𝑦 𝑥−3 𝑥−3 (𝑥−3)
The base is 4y, and the exponent is 3.
4y is a factor 3 times.

3. Product of Powers Property
When multiplying two of the same bases, add the exponents.
4 2 ∙ 4 3 = 4 5
16 ∙ 64 = 1024
4 5 = 1024
𝑥 6 ∙ 𝑥 2 = 𝑥 8
(x ∙ x ∙ x ∙ x ∙ x ∙ x) ∙ (x ∙ x)

4. Power to a Power Property
When you have a power raided to another power, multiply the exponents.
= 4 6
4 2 ∙ 4 2 ∙ 4 2
𝑥 = 𝑥 15
𝑥 3 ∙ 𝑥 3 ∙ 𝑥 3 ∙ 𝑥 3 ∙ 𝑥 3

5. Power of a Product Property
You can “distribute” an exponent to other exponents.
𝑥 2 𝑦 =
𝑥 6 𝑦 4
5 𝑥 2 𝑦 =
25 𝑥 4 𝑦 6

6. Try these… 𝑥 3 ∙ 𝑥 8 𝑥 5 ∙𝑥∙ 𝑥 2 𝑦 2 ∙ 𝑦 −8 ∙ 𝑦 11 𝑏 5 4 𝑎 7 0
𝑏 5 4
𝑎 7 0
6𝑥 𝑦 4 3

7. Multi-step Problems
𝑎 ∙ 𝑎 5 3
4 𝑥 ∙ 5𝑥 3
−2𝑥 3 ∙ 𝑥 4 −2

8. Quotient of Powers Property
When dividing two of the same bases, subtract the exponents.
3∙3∙3∙3∙3 3∙3
3 3 =27
𝑥 8 𝑥 3
𝑥∙𝑥∙𝑥∙𝑥∙𝑥∙𝑥∙𝑥∙𝑥 𝑥∙𝑥∙𝑥
𝑥 5

9. Power of a Quotient Property
You can “distribute” an exponent to all the other exponents in a fraction.
9 16
𝑥 5 𝑦
𝑥 20 𝑦 12

10. Negative Power of a Quotient Property
If a fraction is raised to a negative exponent, flip the fraction and make the exponent positive.
2 5 −3 =
𝑥 4 𝑦 7 −2
𝑦 7 𝑥
𝑦 14 𝑥 8

11. Try these… 𝑥 8 𝑥 6 𝑥 7 𝑥 10 𝑥 5 𝑥 9 𝑥 4 𝑦 3 𝑥 5 𝑦 2 3 2 𝑥 4 𝑦 2 3
𝑥 8 𝑥 6
𝑥 7 𝑥 10
𝑥 5 𝑥 9 𝑥 4 𝑦 3
𝑥 5 𝑦
2 𝑥 4 𝑦
𝑥 2 𝑦 6 −5