Answer
$\sqrt[12]{6^7}$
Work Step by Step
Recall the rational exponent property (pg. 382):
$\sqrt[n]{a}=a^{\frac{1}{n}}$
Applying this property, we get:
$\left(\sqrt[4]{6}\right)\left(\sqrt[3]{6}\right)=6^{\frac{1}{4}}\cdot 6^{\frac{1}{3}}$
Next, recall the basic exponent property (pg. 360):
$a^ma^n=a^{m+n}$
Applying this property to the expression above, we get:
\begin{align*}
6^{\frac{1}{4}}\cdot 6^{\frac{1}{3}}&=6^{\frac{1}{4}+\frac{1}{3}}\\
&=6^{\frac{3}{12}+\frac{4}{12}}\\
&=6^{\frac{3+4}{12}}\\
&=6^{\frac{7}{12}}\\
\end{align*}
Now, recall the rational exponent property (pg. 382):
$a^{\frac{m}{n}}=\sqrt[n]{a^m}=(\sqrt[n]{a})^m$
We use this property to rewrite the result as a radical:
$6^{\frac{7}{12}}=\sqrt[12]{6^7}$
