Answer
$\dfrac{1}{y^2}$
Work Step by Step
Using the laws of exponents, the given expression, $
\dfrac{(y^3)^4}{(y^2)^7}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{y^{3(4)}}{y^{2(7)}}
\\\\=
\dfrac{y^{12}}{y^{14}}
\\\\=
y^{12-14}
\\\\=
y^{-2}
\\\\=
\dfrac{1}{y^2}
.\end{array}