1. Bell Quiz

2. Objectives Simplify exponential expressions. Discuss the definitions of base, power, and exponent.

3. Simplifying Expressions Using the Product Property of Exponents An exponent can be used to show repeated multiplication. The base of a power is the number used as a factor. The exponent is a natural number that indicates how many times the base is used as a factor. (base) 5 3 (exponent)

4. Simplifying Expressions Using the Product Property of Exponents WordsPowerMultiplicationValue Five to the first power5151 55 Five to the second power or five squared 5252 5 ∙ 525 Five to the third power or five cubed 5353 5 ∙ 5 ∙ 5125 Five to the fourth power 5454 5 ∙ 5 ∙ 5 ∙ 5625

5. Example 1 Simplifying Expressions with Exponents Simplify each expression a.7 3 b.(0.3) 4 c.(1/2) 5 d.10 3

6. Lesson Practice Simplify each expression a.6 4 b.(1.4) 2 c.(2/5) 3 d.10 6

7. Simplifying Expressions Using the Product Property of Exponents The product of powers whose bases are the same can be found by writing each power as repeated multiplication. 5 4 ∙ 5 5 = (5 ∙ 5 ∙ 5 ∙ 5) ∙ (5 ∙ 5 ∙ 5 ∙ 5 ∙ 5) = 5 9 The sum of the exponents in the factors is equal to the exponent in the product.

8. Product Property of Exponents If m and n are real numbers and x ≠ 0, then x m ∙ x n = x m+n

9. Example 2 Applying the Product Property of Exponents Simplify each expression. a.x 5 ∙ x 7 ∙ x 2 b.m 3 ∙ m 2 ∙ m 4 ∙ n 6 ∙ n 7

10. Lesson Practice Simplify each expression. a.w 3 ∙ w 5 ∙ w 4 b.y 6 ∙ y 5 ∙ z 3 ∙ z 11 ∙ z 2