Positive Integer Exponents
Meaning
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)
Rules
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.