What are exponents? Exponents are numbers that show how many times a base is used as a factor. How...

What are exponents? Exponents are numbers that show how

many times a base is used as a factor. How do we use exponents?

Exponents will tell us how many times to multiply the base number.

43 exponent

base

24

2 x 2 x 2 x 2 4 x 2 x 2 8 x 2 16

63

6 x 6 x 6 36 x 6 216

You’ve already learned how to use exponents to indicate repeated multiplication.

What happens when you multiply two powers with the same base? Ex. 72 73

Ex. 72 73

(7 7) (7 7 7) 75

Notice that 72 73 = 75,So, when you multiply powers with the same base, you can add

the exponents. 72 73 = 72 + 3 = 75

To multiply numbers or variables with the same base, add the exponents.

Arithmetic Algebra 23 24 am an

23 + 4 am + n

27

3 33 a5 a b2

You can find the power of a power by using the rule for Multiplying Powers with the Same Base like in Part I.

(72)3 = (72)(72)(72) *Notice that you can raise 72 + 2 + 2 a power to a power

by 76 multiplying the

exponents (72)3 = 72 3 =

76

Arithmetic (23)4

23 4

212

Algebra (am)n

am n

(32)3 (a6)2