What is the simplified form of $\left\{(x^m)^{\frac{1}{m}}\right\}^{\frac{1}{m+1}}$?

Use the power law repeatedly: $(a^p)^q=a^{pq}$. Here, $\left\{(x^m)^{1/m}\right\}^{1/(m+1)}=x^{m\cdot \frac{1}{m}\cdot \frac{1}{m+1}}=x^{1/(m+1)}$. Wait carefully: after simplifying $(x^m)^{1/m}=x$, raising that to $1/(m+1)$ gives $x^{1/(m+1)}$. So the correct answer is B if the expression is read exactly as printed. The source solution appears to correspond to a different expression. Hence the mathematically correct simplification is $x^{1/(m+1)}$.