[tex]\dfrac{a^b}{a^c}=a^{(b-c)}[/tex]
An exponent represents repeated multiplication. For example, ...
... x^3 = x·x·x
... x^2 = x·x
If we divide these, the x's in the denominator cancel an equal number in the numerator:
... (x·x·x)/(x·x) = x
If we represent the repeated multiplication using exponents, we can represent the cancellation by subtraction:
... (x^3)/(x^2) = x^(3-2) = x^1 = x
Once we have this idea in mind that division can be done by subtracting denominator exponents, we can use it regardless of the magnitude or sign of the exponents involved.
