1. Lesson 8.2 Apply Exponent Properties Involving Quotients
Essential Question: How do you use the properties of exponents involving quotients?

2. Before we start…
Write out the numerator and denominator as a product and divide out the common factors.

3. Quotient of Powers Property
Words
To divide two powers with the same nonzero base, subtract the exponent of the denominator from the exponent of the numerator.
Algebra
𝑎 𝑚 𝑎 𝑛 = 𝑎 𝑚−𝑛
Numbers
= 4 7−4 = 4 3

4. Power of a Quotient Property
Quotient of Powers Property
Words
To find a power of a quotient, find the power of the numerator and the power of the denominator and divide.
Algebra
𝑎 𝑏 𝑚 = 𝑎 𝑚 𝑏 𝑚
Numbers =

5. How do you use the properties of exponents involving quotients?
To divide two powers with the same nonzero base, subtract the exponent of the denominator from the exponent of the numerator.
To find a power of a quotient, find the power of the numerator and the power of the denominator and divide.

6. Simplify
𝑥 12 𝑥 7 𝑎 6 𝑎 4
𝑤 15 𝑤 9
𝑑 8 𝑑

7. Simplify
𝑏 24 𝑏 10 𝑐 12 𝑐 11
𝑢 16 𝑣 8 𝑢 6 𝑣 2
𝑎 17 𝑏 20 𝑎 5 𝑏 14

8. Simplify
𝑞 3 ∙ 𝑞 5 𝑞 4
𝑎 2 𝑏 8 𝑏 2

9. Simplify
𝑝 6 𝑞 4 ∙ 𝑝 3 𝑞 7 𝑝 𝑞 3
𝑚 8 𝑛 13 𝑛 9

10. Simplify
4 7 𝑐 𝑐 3
8 5 𝑔 𝑔 2

11. Simplify
𝑥 𝑦 3
− 7 𝑥 2

12. Simplify
4 𝑥 2 5𝑦 3
𝑎 2 𝑏 5 ∙ 1 2 𝑎 2

13. Simplify
2𝑥 2 𝑦 ∙ 1 4 𝑥 5

14. Simplify
𝑥 𝑦 𝑦 2 𝑥 𝑧 4

15. How do you use the properties of exponents involving quotients?

16. Ticket Out the Door
Simplify
𝑥 6 𝑦 8 𝑥 3 𝑦 2