8-1 Zero and Negative Exponents & 8-3 Multiplication Properties of Exponents

Day 38

Objective: 1.01

Investigation: 23 = 2 . 2 . 2 = Do you see a 22 = 2 . 2 = pattern? 21 = 2 Keep it going! 20 = 2-1 = 2-2 = 2-3 =

Notes

Exponents

2x3

2 is the coefficient,

x is the base and

3 is the exponent

Zero as an Exponent

a0 = 1

Negative Exponent

a-1 =

a

1

Examples: Simplify

1) 3-4

2) (-4)-3

3) -3-2

4) ½ -3

5) (-5)0

6) 3ab-2

7)

8)

x3

1

yx5

6

Examples

Evaluate if n = -2 and w = 5.

nw4

0

9) n-3w0 11)

10) 12)

wn

2

1

nw2

1

Multiplying Powers with the SAME BASE 23 . 24 =

WRITE IT OUT 4 . 43 . 42 = IN EXPANDED

FORM!

Notes

Multiplying Powers of the Same Base

am • an = am+n

Examples

Rewrite using each base only once.

13) 53 x 56

14) 24 x 2-3

15) 7-3 x 72 x 76

Examples

Simplify

16) a • a5 19) a • b • a5

17) n2 • n3 • 7n 20) 2y3 • 7x2 • 2y4

18) 6y2 • 3y3 • 2y-4 21) m2 • n-2 • 7m