Provide an appropriate response.
-$\sqrt [ 3 ] { 2 } \cdot \sqrt [ 4 ] { 12 }$
A) $\sqrt [ 7 ] { 27,648 }$
B) $\sqrt [ 7 ] { 24 }$
C) $\sqrt [ 12 ] { 27,648 }$
D) $\sqrt [ 12 ] { 24 }$

Question

Quizplus · Accepted Answer

We can simplify the expression by finding a common denominator for the exponents:

\begin{align*}
\sqrt[3]{2} \cdot \sqrt[4]{12} &= \sqrt[3 \cdot 4]{2^4} \cdot \sqrt[3 \cdot 4]{12^3} \
&= \sqrt[12]{2^4 \cdot 12^3} \
&= \sqrt[12]{2^2 \cdot 2^2 \cdot 2^2 \cdot 2 \cdot 2 \cdot 3^3} \
&= \sqrt[12]{(2^2 \cdot 3)^3 \cdot 2 \cdot 2} \
&= \sqrt[12]{36^3 \cdot 4} \
&= \sqrt[12]{46,656} \
&= \boxed{	extbf{(C) } \sqrt[12]{27,648}}
\end{align*}

Provide an Appropriate Response 23⋅124\sqrt [ 3 ] { 2 } \cdot \sqrt [ 4 ] { 12 }32​⋅412​

Provide an Appropriate Response $\sqrt [ 3 ] { 2 } \cdot \sqrt [ 4 ] { 12 }$