Exponential function/Base/Rational exponent/Compatible/Exercise

Let ${}a>0$ and let ${}q={\frac {r}{s}}$ be a rational number. Show that the expression

${}a^{q}={\sqrt[{s}]{a^{r}}}\,$

is compatible with the definition

${}a^{q}=\exp(q\ln a)\,.$

Create a solution