Let's see why that happens by evaluating an expression with exponents.
[tex]\frac{a^{20}}{a^{10}}[/tex] <-- Now expand the exponent
[tex]\frac{a^{20}}{a^{10}} = \frac{(a)(a)(a)(a)(a)(a)(a)(a)(a)(a)(a)(a)(a)(a)(a)(a)(a)(a)(a)(a)}{(a)(a)(a)(a)(a)(a)(a)(a)(a)(a)}[/tex]
Now simplify the fraction by canceling out any common factors on the numerator and denominator.
[tex]\frac{(a)(a)(a)(a)(a)(a)(a)(a)(a)(a)(a)(a)(a)(a)(a)(a)(a)(a)(a)(a)}{(a)(a)(a)(a)(a)(a)(a)(a)(a)(a)} = \frac{(a)(a)(a)(a)(a)(a)(a)(a)(a)(a)}{1} = a^{10}[/tex]
So, it's the same thing as subtracting the powers.
