Find $x$ such that $\sqrt[x]9=81$ Find $x$ such that $\sqrt[x]9=81$
If I simplified this to $9^{\frac1x}=81$, then we have $x={\frac12}$
I'm stuck here,
My question:  can we rewrite $\sqrt[\frac{a}{b}] c\quad$ as $\sqrt[a]{c^b}\quad$ for all positive  real number $c$?

Yes you can! Note that $$\sqrt[\frac a b]c=c^{\frac {1} {\frac a b}}=c^{\frac b a}=\sqrt[a]{c^b}$$
