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.
