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) $m+n$

Question

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) $m+n$

Quizplus · Accepted Answer

To eliminate the radicals, you need to raise both sides to the least common multiple (LCM) of the indices of the radicals, which in this case are $m$ and $n$. Since $m$ and $n$ are relatively prime, their LCM is simply their product, $mn$.

What Is the Smallest Power to Which You Can Raise 7x+1n=−9−8xm\sqrt[n]{7 \mathrm{x}+1}=\sqrt[m]{-9-8 \mathrm{x}}n7x+1​=m−9−8x​

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