Answer
$\dfrac{a^{18}}{b^{48}}$
Work Step by Step
Using $\left(\dfrac{a}{b}\right)^x=\dfrac{a^x}{b^x}$, then the expression, $
\left(\dfrac{a^3}{b^8}\right)^6
$, simplifies to
\begin{array}{l}\require{cancel}
\dfrac{(a^3)^6}{(b^8)^6}
.\end{array}
Using $(a^x)^y=a^{xy}$, then the given expression, $
\dfrac{(a^3)^6}{(b^8)^6}
$, simplifies to
\begin{array}{l}\require{cancel}
\dfrac{a^{3(6)}}{b^{8(6)}}
\\\\=
\dfrac{a^{18}}{b^{48}}
.\end{array}
