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32 = 3
´
3
33 = 3
´
3 ´
3
In
general xn = x
· x · x · . . . · x
(n factors of x)
x is the base, and n is the exponent (or power)
Product
of Different Powers: aman = am + n
- IMPORTANT:
all the numbers must have the same bases
(the same ‘a’)
-
Example:
(42)(43) = 45
This
is easy to see if you write out the exponents:
(42)(43) = (4
· 4) · (4 · 4 · 4) = 4 · 4 ·
4 · 4 · 4 = 45
WARNING:
Do not attempt to use this rule for addition:
42 + 43 is NOT 45.
In fact there is no way to simplify xn + xm
if n and m are different powers.
Power
Raised to a Power: 
Example:
(42)3 = 46
This
is also easy to see if you expand the
exponents:
(42)3 = (42)(42)(42)
= (4 · 4) (4 · 4)
(4 · 4)
= 4 · 4 · 4 · 4 · 4 · 4
= 46
There are more rules for combining numbers with exponents, but this is
enough for now.
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