Combine the following expressions. (Assume any variables under an even root are nonnegative.)

Question

Quizplus · Accepted Answer

The expressions can be combined by simplifying the even roots. The first expression can be written as $\sqrt[4]{\frac{a^2b^6}{c^6}}$ and the second expression can be written as $\sqrt[4]{\frac{a^2b^2}{c^2}}$. Combining the expressions gives us $\sqrt[4]{\frac{a^2b^6}{c^6}}\cdot\sqrt[4]{\frac{a^2b^2}{c^2}}=\sqrt[4]{\frac{a^4b^8}{c^8}}=\sqrt[4]{\left(\frac{ab^2}{c^2}ight)^4}$. Thus, the answer is $\boxed{	extbf{(C)}}$.

Combine the Following Expressions