What Is the Smallest Power to Which You Can Raise $\sqrt[n]{7 \mathrm{x}+1}=\sqrt[m]{-9-8 \mathrm{x}}$

Multiple Choice

What is the smallest power to which you can raise both sides of the radical equation
$\sqrt[n]{7 \mathrm{x}+1}=\sqrt[m]{-9-8 \mathrm{x}}$ so that the radicals are eliminated. Assume that $\mathrm{m}$ and $\mathrm{n}$ are relatively prime.

A) $\mathrm{mn}$

B) $\frac{m+n}{m n}$

C) $\frac{1}{m}+\frac{1}{n}$

D) $m+n$