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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