1. Warm Up
Simplify. 1. 3. 5.
(10²)³ 2. 4. 6.

2. Division Properties of Exponents
Objective
Use division properties of exponents to evaluate and simplify expressions.

3. A quotient of powers with the same base can be found by writing the powers in a factored form and dividing out common factors.
Notice the relationship between the exponents in the original quotient and the exponent in the final answer: 5 – 3 = 2.
Copy

4. Finding Quotients of Powers
Simplify. A. B.

5. Finding Quotients of Powers
Copy
Finding Quotients of Powers
Simplify. C. D.

6. Both and 729 are considered to be simplified.
Helpful Hint

7. Try This!
Simplify. a. b.

8. Try this!
Simplify. c. d.

9. A power of a quotient can be found by first writing the numerator and denominator as powers.
Notice that the exponents in the final answer are the same as the exponent in the original expression.
Copy

10. Finding Positive Powers of Quotient
Simplify.
Use the Power of a Quotient Property.
Simplify.

11. Finding Positive Powers of Quotient
Copy
Finding Positive Powers of Quotient
Simplify.
Use the Power of a Product Property.
Use the Power of a Product Property:
Simplify and use the Power of a Power Property:

12. Finding Positive Powers of Quotient
Copy
Finding Positive Powers of Quotient
Simplify.
Use the Power of a Product Property.
Use the Power of a Product Property:
Use the Power of a Product Property:
Use the Power of a Product Property:

13. Try This!
Simplify.
Use the Power of a Quotient Property.
Simplify.

14. Try this!
Simplify.

15. Try This!
Simplify.

16. Copy

17. Finding Negative Powers of Quotients
Copy
Finding Negative Powers of Quotients
Simplify.
Rewrite with a positive exponent.
Use the Powers of a Quotient Property .
and

18. Finding Negative Powers of Quotients
Simplify.

19. Finding Negative Powers of Quotients
Copy
Finding Negative Powers of Quotients
Simplify.
Rewrite each fraction with a positive exponent.
Use the Power of a Quotient Property.
Use the Power of a Product Property:
(3)2 (2n)3 = 32  23n3
and (2)2  (6m)3 = 22  63m3

20. Finding Negative Powers of Quotients
Copy
Finding Negative Powers of Quotients
Simplify.
Square and cube terms. 1 24 2 12
Divide out common factors.
Simplify.

21. Whenever all of the factors in the numerator or the denominator divide out, replace them with 1.
Helpful Hint

22. Try This!
Simplify.
Rewrite with a positive exponent.
Use the power of a Quotient Property.
93=729 and 43 = 64.

23. Try This!
Simplify.
Rewrite with a positive exponent.
Use the Power of a Quotient Property.
Use the Power of a Power Property: (b2c3)4= b2•4c3•4 = b8c12 and (2a)4= 24a4= 16a4.

24. Try This!
Simplify.
Rewrite each fraction with a positive exponent.
Use the Power of a Quotient Property.
Use the Power of a Product Property: (3)2= 9.
Add exponents and divide out common terms.