3.2 Exponent Laws Part 2 February 26, 2013

More Exponent

Rules!

Example 1:

(22)3

Write as expanded multiplication and then as a single power.

What do you notice?

3.2 Exponent Laws Part 2 February 26, 2013

What do you notice?

An Experiment

1. Choose a base2. Choose an exponent3. Raise that to a more different exponent.

Raising a Power to an Exponent(am)n = amn

When a power is raised to an exponent, multiply the exponents to write the expression with a single exponent.

3.2 Exponent Laws Part 2 February 26, 2013

Write the following expressions as a single power, and then evaluate

a) (22)3

b) (33)2

c) [(­3)4]3

Raising a Product to an Exponent

(ab)m = ambm

When a product is raised to an exponent, you can rewrite each factor in the product with the same

exponent.

3.2 Exponent Laws Part 2 February 26, 2013

Does it work?!

(4 × 2)3 = 43 ⋅ 23

Let's check if this works!

Method 1: Using order of operations:

Method 2: Using order of operations:

?

Write the following expressions as the product of two powers, and then evaluate

a) (3(­2))3

b) (5 x 4)4

c) [(­3) x 7]2

3.2 Exponent Laws Part 2 February 26, 2013

Raising a Quotient to an Exponent

b ≠ 0

When a quotient is raised to an exponent you can write each number in the quotient with the same exponent.

Does it work?!

(4 ÷ 2)3 = 43 ÷ 23

Let's check if this works!

Method 1: Using order of operations:

Method 2: Using order of operations:

?

3.2 Exponent Laws Part 2 February 26, 2013

Write the following expressions as the product of two powers, and then evaluate

a) (3 ÷ 2)3

b) (2 ÷ 5)5

c) [(­3) ÷ 7]2