|
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. |
