All the exponent laws are stated below, for completeness.
This web exercise gives practice with:
[beautiful math coming... please be patient]
$$
\frac{x^m}{x^n} = x^{m-n}
$$
Here's the motivation for this exponent law:
[beautiful math coming... please be patient]
$$
\frac{x^5}{x^2}
= \frac{x\cdot x\cdot x\cdot x\cdot x}{x\cdot x}
= x\cdot x\cdot x
= x^3
= x^{5-2}
$$
$x^mx^n = x^{m+n}$ | Verbalize: same base, things multiplied, add the exponents |
$\displaystyle \frac{x^m}{x^n} = x^{m-n}$ | Verbalize: same base, things divided, subtract the exponents |
$(x^m)^n = x^{mn}$ | Verbalize: something to a power, to a power; multiply the exponents |
$(xy)^m = x^my^m$ | Verbalize: product to a power; each factor gets raised to the power |
$\displaystyle \left(\frac{x}{y}\right)^m = \frac{x^m}{y^m}$ | Verbalize: fraction to a power; both numerator and denominator get raised to the power |