For all numbers x (not zero) and all integers m and n,

When you divide,
and the bases are the same,
you SUBTRACT the exponents.
(top exponent minus bottom exponent)

When in doubt, expand the terms (as shown at the right) to see what is happening.

Examples:

1. The bases are the same (both 2's), so the exponents are subtracted.

2. ^{
}The bases are the same (all a 's), so the exponents are subtracted. Notice how the numbers in front of the bases (6 and 1) are being divided.

3.
The bases are the same (all x's), so the exponents are subtracted.The numbers in front of the bases are divided.

4. Remember: top exponent minus bottom exponent.
Remember: raising to a 0 power creates a 1.

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