Answer
$\color{blue}{\dfrac{1}{y^{10}}}$
Work Step by Step
RECALL:
(1) $a^{-m} = \dfrac{1}{a^m}$
(2) $\dfrac{a^m}{a^n} = a^{m-n}$
(3) $\left(\dfrac{a}{b}\right)^m=\dfrac{a^m}{b^m}$
(4) $(ab)^m = a^mb^m$
(5) $(a^m)^n=a^{mn}$
(6) $a^m \cdot a^n = a^{m+n}$
(7) $a^0=1, a\ne0$
Use rule (4) above to obtain:
$=\dfrac{(8^{-4}(y^2)^{-4}) \cdot (8^{-2}(y^5)^{-2})}{(8^{-3})^{2}(y^{-4})^2}$
Use rule (5) above to obtain:
$=\dfrac{8^{-4}y^{2(-4)}\cdot (8^{-2}(y^{5(-2)})}{8^{-3(2)}y^{-4(2)}}
\\=\dfrac{8^{-4}y^{-8} \cdot 8^{-2}y^{-10}}{8^{-6}y^{-8}}$
Use rule (6) above to obtain:
$=\dfrac{8^{-4+(-2)}y^{-8+(-10)}}{8^{-6}y^{-8}}
\\=\dfrac{8^{-6}y^{-18}}{8^{-6}y^{-8}}$
Use rule (2) above to obtain:
$=8^{-6-(-6)}y^{-18-(-8)}
\\=8^{-6+6}y^{-18+8}
\\=8^0y^{-10}$
Use rule (7) to obtain:
$\\=1\cdot y^{-10}
\\=y^{-10}$
Use rule (1) above to obtain:
$\\=\color{blue}{\dfrac{1}{y^{10}}}$
