1. Division Properties of Exponents
Lesson 4.2
Division Properties of Exponents

2. Warm-Up
Simplify.
(3x4)2
(2a7b)(5a2b4)
2y3 ∙ (4y5)2
9x8
10a9b5
32y13

3. Division Properties of Exponents
Lesson 4.2
Division Properties of Exponents
Use properties of exponents to simplify expressions involving division.

4. Simplify the fractions by cancelling common factors.
Good to Know!
You have learned that when two powers with the same base are multiplied, the base remains the same and the exponents are added together. Examine the division problems below. When two powers with the same base are divided, the base remains the same and the exponents are subtracted. You can also simplify a power of a quotient or fraction by “distributing” the power to both the numerator and denominator.
Simplify the fractions by cancelling common factors.

5. Division Properties of Exponents
Quotient of Powers To divide two powers with the same base, subtract the exponents. Power of a Quotient To find the power of a quotient, find the power of the numerator and denominator.

6. Examples 1 & 2
Simplify the following. a. b.

7. Example 1
Simplify the following. a. Group powers that have the same base. Subtract exponents.

8. Example 2
Simplify the following. b. Distribute the power to each base. Multiply powers of powers and evaluate coefficients.

9. More Properties of Exponents
Negative Exponents For any nonzero number a and integer n, the expression a −n is the reciprocal of an. Also, an is the reciprocal of a −n. Zero Exponents Any nonzero number, a, raised to the zero power is 1. Good to Know! An expression is in simplest form only if it has no negative or zero exponents. An exponent with its base can be moved to the opposite side of the fraction bar to change its sign.

10. Example 3
Simplify the following. a. Any term to the power of 0 equals 1.

11. Example 4
Simplify the following.

12. Example 4 Continued…
Simplify the following. b. Write as separate factors. Use the rules for negative exponents. Multiply factors.

13. Example 5: CHALLENGE
Simplify the following. c. Write as separate factors and group like bases. Simplify by subtracting exponents and dividing coefficients.

14. Example 5 Continued
Simplify the following. c. Use rules for zero and negative exponents. Simplify.

15. 4.2 Formative Assessment
Simplify.