Transcript EXPONENTS AND MULTIPLICATION 4-7

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What are exponents?
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Exponents are numbers that show how many
times a base is used as a factor.
How do we use exponents?
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Exponents will tell us how many times to
multiply the base number.
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43  exponent
base
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24
2x2x2x2
4 x 2x2
8 x 2
16
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63
6x6x6
36 x 6
216
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You’ve already learned how to use
exponents to indicate repeated
multiplication.
What happens when you multiply two
powers with the same base?
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Ex. 72 73
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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
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To multiply numbers or variables with the
same base, add the exponents.
Arithmetic
Algebra
23 24
am an
23 + 4
am + n
27
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3 33
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a5 a b2
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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
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Arithmetic
(23)4
23 4
212
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Algebra
(am)n
am n
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(32)3
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(a6)2