Working with Powers Integer Exponents Exponent Rules Order

Working with Powers • Integer Exponents • Exponent Rules • Order of Operations 5/21/2021 1

• 2× 2= • 2× 2× 2× 2= • How can we write these in shorter notation? 5/21/2021 2

• Multiplication is a shortcut for repeated addition. 3+3+3=5× 3 • Exponents are a shortcut for repeated multiplication. 3× 3× 3= 5/21/2021 3

Write these numbers using exponential notation: • 10, 000 = 10? • 27 = 3? • 32 = 2? 5/21/2021 4

Integer Exponents • Base 4 • Exponent 3 • 43 is called a power • 43 = 4 x 4 • = 64 5/21/2021 5

You try these. . . • 72 • 4 5 • 10 2 5/21/2021 6

Operations with Exponents • Multiply (x 3)∙(x 4) = (x ∙ x) ∙ (x ∙ x ∙ x) = (x ∙ x ∙ x ∙ x) = x 7 A 5 ∙ A 4 = • Divide: 5/21/2021 7

Exponent Rules #1 n times 5/21/2021 8

Zero as an exponent • 40 • 0 9 • 0 17 5/21/2021 9

Exponent Rules #2 5/21/2021 10

a 0 = 1 • M 0 • (pq)0 • (2 x 2 y)0 5/21/2021 11

Negative Exponents • -1 3 • -4 2 • 7 -1 • (1/2) -1 • 5 -2 • (3/4) -2 5/21/2021 12

Exponent Rules #3 5/21/2021 13

• M-2 • x-5 • (1/y)-3 5/21/2021 14

Combining Exponents m n a a =? 5/21/2021 15

Exponent Rules #4 5/21/2021 16

• x 5 x 4 • y-2 y 7 • b 3 b-6 • m 6 m-6 • • 2 z-3 z 5 w-6 w-2 (2 x 3)(4 x-2) 5/21/2021 17

Combining Exponents am/an=? 5/21/2021 18

Exponent Rules #5 5/21/2021 19

5/21/2021 20

Combining Exponents (am)n=? 5/21/2021 21

Exponent Rules #6 5/21/2021 22

• (w 4)5 • (p-3)4 • (5 x 4)-2 • (-3 y-7)3 5/21/2021 23

Combining Exponents 5/21/2021 24

Exponent Rules #7 (distributive rule for exponents) 5/21/2021 25

5/21/2021 26

Exponent Rules • 1. • 2. • 3. 5/21/2021 27

Exponent Rules • 4. • 6. • 5. • 7. 5/21/2021 28