Warm Up Evaluate b 2 for b = 4 4. n 2 r for n = 3 and r =

Lesson 4.3: Powers of Exponents

Objectives Multiply, divide, and simplify rational numbers by using exponent rules (NS 2.3). Understand negative whole-number exponents. (NS 2.1)

Parts of a power Parts of a power A power has two parts: a base and an exponent. Baserepresents the repeated factor in the product Exponent represents the number of times the base is repeated as a factor in the product. Base   Exponent Factors =a●a●a●a a4a4 Read, “a to the forth power.”

Multiplying Powers with the same base (a ●a ● a ● a ●a) ●(a ● a ● a) a 5 ●a 3 = 5 factors 3 factors 8 factors = a 8 Notice: The exponent of a is 8, which is equal to

a) b) x9 x c) = 22+2= 24 = 16 = x9+1 =x10 1 = = 34 = 81 Rule #1When multiplying powers with the same base, ADD the exponents. Rule #1: When multiplying powers with the same base, ADD the exponents. a m a n = a m + n

1 Now you try.

2x 2 3x 4 Using repeated multiplication Using exponent rule = (2 x x) (3 x x x x) = 6x 6 = (2 3) (x 2 x 4 ) = 6x a m a n = a m + n Multiplying Variable Expressions

Simplify. Simplifying Variable Expressions

Raising a Power with a Power A. (5 4 ) 2 (5 4 ) B. (6 7 ) 9 (6 7 ) Simplify each expression. Write your answer in exponential form. C. D. (17 2 ) – –20 17 – – –36 Multiply exponents.

c5c5 c3c3 = c c c c c c c c copies of c 5 copies of c Dividing Powers with the same base =c c=c 2 Notice: The exponent of c is 2, which is equal to 5-3

Rule #2 Rule #2: When dividing powers with the same base, SUBTRACT the exponents of the denominator from the exponent of the numerator. amam anan = a m - n = a) b) 8x 8 4x 3 = 2x = 2 2 = x 6 x5y4x5y4 x3yx3y = x 5 -3 y 4-1 =x 2 y 3 c)

Now you try

Summary When multiplying powers with the same base, keep the base and add the exponents. When dividing powers with the same base, keep the base and subtract the exponents.

Lesson Quiz n 7 1. n 3  n t t 9 t 7 6. (m 2 ) 19 m (9 -8 ) 9 8. (10 4 ) 0 1 Simplify each expression. Write your answer in exponential form