Answer
$y^{5a+6}$
Work Step by Step
Using the laws of exponents, the given expression, $
\dfrac{ \left( y^{3a} \right)^2}{y^{a-6}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{ y^{3a(2)}}{y^{a-6}}
\\\\=
\dfrac{ y^{6a}}{y^{a-6}}
\\\\=
y^{6a-(a-6)}
\\\\=
y^{6a-a+6}
\\\\=
y^{5a+6}
.\end{array}
