Essential Question: What is the first step for simplifying an exponential expression that contains negative exponents?

1) Zero as an exponent Any number to the 0 power equals 1 Why?▪ x3 = 1x • 1x • 1x▪ x7 = 1x • 1x • 1x • 1x • 1x • 1x • 1x▪ x0 = no “x”s, so we leave just a “1”

2) Negative exponents Any number to a negative exponent moves

the base to the opposite side of a fraction, and the exponent becomes positive

Simplify: 4-3

Negative exponent. Move the base.

34

1341

Make the exponent positive.

1

64

Simplifying Expressions Simplify 4y0x-3

4 0y 3x

Exponent of 0 = 1

1

Move negative exponentMake exponent positive

3x 3

4

x

YOUR TURN – Simplify each expression 3-4

-70

11m-5

0 5

1 2

7

2

s t

m

1

2 5 2 5

7 2 1 14

m t m t

5

11

m

4

1 1

3 81

1

Multiplying Same Bases (add) When two numbers are multiplied

together and have the same base, their exponents are added.

Why?▪ x3 = x • x • x▪ x5 = x • x • x • x • x▪ x3 • x5 = x • x • x • x • x • x • x • x = x8

▪ x3 • x5 = x3+5 = x8

Dividing Same Bases (subtract) When two numbers are divided and have the

same base, their exponents are subtracted. Why?▪ x3 = x • x • x▪ x5 = x • x • x • x • x▪

2

5 2

5

35 2

3

3

1 1

1

x x x x x

x x x x

x x x

x xx

x

x

x

Power to a power (multiply) If an exponent is raised to a power

(typically outside a parenthesis), multiply the exponents together.

Examples:▪ (3x2y3)4 = 34x8y12

= 81x8y12

▪ 31 3 3 6

2 6 3

2 ( 2) 8x x y

y y x

YOUR TURN – Simplify each expression (7a2)(-2a-5)

5 2

3 2

2ab c

a bc

42 4 0

2

22

ba b c

a

33

1414a

a

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