Perform the indicated operation and express your answer in simplest radical form. $\frac { \sqrt [ 3 ] { 8 } } { \sqrt [ 4 ] { 8 } }$
A) $- \sqrt { 8 }$
B) $\sqrt [ 12 ] { 8 }$
C) $\frac { 1 } { \sqrt [ 12 ] { 8 } \sqrt { 8 } }$
D) $\sqrt [ 7 ] { 8 }$
E) $\sqrt [ 12 ] { 64 }$

Question

Quizplus · Accepted Answer

We can simplify the expression by using the property $\sqrt[a]{x}=\sqrt[b]{x^{bc}}$ where $b$ and $c$ are integers such that $a=bc.$ In this case, we have:

\begin{align*}
\frac{\sqrt[3]{8}}{\sqrt[4]{8}} &= \frac{\sqrt[3]{8}}{\sqrt[4]{8}\cdot \sqrt[4]{8}} \
&= \frac{\sqrt[3]{2^3}}{\sqrt[4]{2^3\cdot 2}} \
&= \frac{2}{\sqrt[4]{2^4}}\
&= \frac{2}{2}\
&= \boxed{	extbf{(B) } \sqrt[12]{8}}.
\end{align*}

Perform the Indicated Operation and Express Your Answer in Simplest 8384\frac { \sqrt [ 3 ] { 8 } } { \sqrt [ 4 ] { 8 } }48​38​​

Perform the Indicated Operation and Express Your Answer in Simplest $\frac { \sqrt [ 3 ] { 8 } } { \sqrt [ 4 ] { 8 } }$