Question 159·Medium·Advanced Math

The bottom number $6$ means a sixth root: $m^{1/6}=\sqrt[6]{m}$. The condition $m>0$ means this even root is defined.

Choose $m=64$ because $64=2^6$, so its sixth root is a whole number. Type $m=64$ and $m^{5/6}$ in Desmos; it prints $32$. Don't use $m=1$ for this check: every option equals $1$ there.

The top number $5$ says to raise that sixth root to the fifth power: $m^{5/6}=(\sqrt[6]{m})^5$.

Raising the sixth root to the fifth power gives the same result as taking the sixth root of the fifth power: $(\sqrt[6]{m})^5=\sqrt[6]{m^5}$. Add $\sqrt[6]{m^5}$ in Desmos; it also prints $32$. That check agrees with the exponent rule, which proves the match for every positive $m$. So the equivalent expression is $\sqrt[6]{m^5}$. Choice B.