Answer
$\frac{8}{a^{\frac{1}{12}}}$
Work Step by Step
We will use the rule $\frac{a^{m}}{a^{n}}=a^{m-n}$ in the simplification of the expression:
$\frac{56a^{\frac{1}{6}}}{7a^{\frac{1}{4}}}$
$=\frac{56}{7}\times\frac{a^{\frac{1}{6}}}{a^{\frac{1}{4}}}$
$=8\times a^{\frac{1}{6}-(\frac{1}{4})}$
$=8\times a^{\frac{1(2)-1(3)}{12}}$
$=8\times a^{\frac{2-3}{12}}$
$=8\times a^{\frac{-1}{12}}$
$=\frac{8}{a^{\frac{1}{12}}}$
