Exponents - Basics

Evaluate 3⁰

1

Evaluate (−3) ²

(−3) × (−3) = 9

Evaluate (-3)⁴

(−3) ×( −3) ×(−3) ×( −3) = 81

A negative base to an even power is a positive number:

(−3)² −3 × −3 = 9

A negative base to an odd power is a negative number

(−3)³ (−3) ×( −3) × (−3) = −27

Evaluate 2 −³

1/2³

NOTE: for 0 < x < 1

x² < x < √x example x=.04 , then .0016 < . 04 < .2

NOTE: For 0 < x < 1 x² is less than x,

x² < x, example .5 × .5 = .25

Any number to the zero power

x⁰ = 1

Evaluate ½ ² (½ is between 0 and 1)

½ ² = ½ × ½ = ¼ if you have ½ a cookie, and have to share ½ of that, you have less

Evaluate − 2⁴

− (2 × 2 × 2 × 2) = − 16

For numbers greater than one for x > 1

√x < x < x² example x =4, then 2 < 4 < 16

NOTE: For 0 < x <1 √x is more than x

√x > x example x = .04, then √.04 = .2 > .04 example x = .25, then √.25 = .5 > .25

Evaluate (-5)³

(−5) × (−5) × (−5) = −125

Evaluate 7⁰

1

Evaluate 2 −¹

1/2

Evaluate 2 −²

1/2²

Simplify: 10¹² ÷ 10⁴

10¹²⁻⁴ = 10⁸ Division law of exponents

2⁹ what is the base?

2

Evaluate 2⁵

2 × 2 × 2 × 2 × 2 = 32

-4² what is the base?

4 is the base

Simplify: 4³ x 4⁶

4 ³+⁶= 4⁹ Multiplication law of exponents

3⁵ what is the exponent?

5

Special consideration for numbers less than one but greater than zero

For 0 < x < 1: x could be any number on the number line between 0 and 1

Don't be tricked (−4)² ≠ −4²

Negative bases will be in parenthesis (−4)² = (−4) × (−4) = 16

Simplify: 5³ x 4²

can't use exponent laws because NOT same base (5 ×5 ×5) × (4×4) = 125 × 16 = 2000

−4² = − ( 4 × 4 )= −16

raise 4 to the ² power, then put a negative sign in front of that product.

Simplify: 3² x 3⁶ x 3

remember that 3 = 3¹, therefore 3²⁺⁶⁺¹ = 3⁹