All the exponent laws are stated below, for completeness.
This web exercise gives practice with:
$$
\cssId{s6}{x^mx^n = x^{m+n}}
$$
Here's the motivation for this exponent law:
$$
\cssId{s8}{x^2} \cssId{s9}{x^3}
\cssId{s10}{=
\overset{\text{two factors}}{\overbrace{x\cdot x}}}
\cssId{s11}{\cdot
\overset{\text{three factors}}{\overbrace{x\cdot x\cdot x}}}
\cssId{s12}{\ = \
\overset{\text{five factors}}{\overbrace{x\cdot x\cdot x\cdot x\cdot x}}}
\cssId{s13}{\ = \ x^5}
\cssId{s14}{\ = \ x^{2+3}}
$$
$x^mx^n = x^{m+n}$ | 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 |