Warm Up Evaluate 1 33 2 4 4

Warm Up Evaluate. 1. 33 2. 4 • 4 • 4 27 256 3. b 2 for b = 4 16 4. n 2 r for n = 3 and r = 2 18

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 A power has two parts: a base and an exponent. Exponent a 4 =a●a●a●a Base Factors Read, “a to the forth power. ” Base represents the repeated factor in the product Exponent represents the number of times the base is repeated as a factor in the product.

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

Rule #1: #1 When multiplying powers with the same base, ADD the exponents. am • an = am + n a) 22 • 22 = 22+2 = 24 = 16 b) x 9 1 • x = x 9+1 =x 10 c) 36 • 3 -2 = 36+-2 = 34 = 81

Now you try. 1

Multiplying Variable Expressions am • an = am + n Using repeated multiplication 2 x 2 • 3 x 4 = (2 • x) • (3 • x • x) = 6 x 6 Using exponent rule 2 • x 4) 2 + 4 = 6 x 6 2 4 = (2 • 3) • (x = 6 x 2 x • 3 x

Simplifying Variable Expressions Simplify.

Raising a Power with a Power Simplify each expression. Write your answer in exponential form. A. (54)2 D. (172)– 20 C. (54)2 54 • 2 58 B. (67)9 67 • 9 663 2 3 12 • – 36 172 • – 20 17– 40 Multiply exponents.

Dividing Powers with the same base 5 copies of c 1 1 1 c 5 c • c • c = c 3 c • c 1 1 = c • c = c 2 1 3 copies of c Notice: The exponent of c is 2, which is equal to 5 -3

Rule #2: #2 When dividing powers with the same base, SUBTRACT the exponents of the denominator from the exponent of the numerator. am = am - n an 25 2 5 3 = 2 a) = 2 23 8 x 8 8 - 2 = x 6 = 2 x b) 3 4 x x 5 y 4 5 -3 4 -1 2 • y 3 = x • y = x c) x 3 y

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 Simplify each expression. Write your answer in exponential form. 1. n 3 n 4 n 7 109 4 3. 105 10 5. 32 • 33 • 35 310 7. (9 -8)9 1 972 2. 8 • 88 4. t 9 t 7 8 t 2 6. (m 2)19 m 38 8. (104)0 1 9