Provide an appropriate response.
-$\frac { \sqrt [ 6 ] { y ^ { 5 } } } { \sqrt [ 8 ] { y ^ { 3 } } }$
A) $\sqrt [ 24 ] { \mathrm { y } ^ { 11 } }$
B) $\frac { \sqrt [ 6 ] { y ^ { 5 } } } { \sqrt [ 8 ] { y ^ { 3 } } }$
C) $\sqrt [ 48 ] { \mathrm { y } ^ { 22 } }$
D) $\sqrt { y }$

Question

Quizplus · Accepted Answer

We can simplify the expression by combining the exponents inside the radicals: $\frac{\sqrt[6]{y^5}}{\sqrt[8]{y^3}}=\sqrt[6-8]{y^{5-3}}=\sqrt[24]{y^2}=\sqrt[24]{y \cdot y}=y^{\frac{1}{24}}$. Therefore, the correct answer is A, $\sqrt[24]{\mathrm{y}^{11}}$, which is equivalent to $y^{\frac{11}{24}}$.

Provide an Appropriate Response y56y38\frac { \sqrt [ 6 ] { y ^ { 5 } } } { \sqrt [ 8 ] { y ^ { 3 } } }8y3​6y5​​

Provide an Appropriate Response $\frac { \sqrt [ 6 ] { y ^ { 5 } } } { \sqrt [ 8 ] { y ^ { 3 } } }$