Answer
$\color{blue}{\dfrac{625}{a^{10}}}$
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) $a^m \cdot a^n = a^{m+n}$
Use rule (4) above to obtain:
$=5^4a^{-1(4)} \cdot a^{2(-3)}
\\=5^4a^{-4} \cdot a^{-6}$
Use rule (6) above to obtain:
$=5^4a^{-4+(-6)}
\\=5^4a^{-10}
\\=625a^{-10}$
Use rule (1) above to obtain:
$=625 \cdot \dfrac{1}{a^{10}}
\\=\color{blue}{\dfrac{625}{a^{10}}}$
