All the exponent laws are stated below, for completeness.
This web exercise gives practice with:
[beautiful math coming... please be patient]
$$
(x^m)^n = x^{mn}
$$
Here's the motivation for this exponent law:
[beautiful math coming... please be patient]
$$
(x^2)^3
= (x^2)(x^2)(x^2)
= \overset{\text{three piles, two in each}}{\overbrace{(x\cdot x)(x\cdot x)(x\cdot x)}}
= x^6
= x^{2\cdot 3}
$$
$x^mx^n = x^{m+n}$ | 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 |