Answer
$\dfrac{(a^{6}b^{-2})^{4}}{(4a^{-3}b^{-3})^{3}}=\dfrac{a^{33}b}{64}$
Work Step by Step
$\dfrac{(a^{6}b^{-2})^{4}}{(4a^{-3}b^{-3})^{3}}$
Evaluate the exponential expressions in the numerator and the denominator:
$\dfrac{(a^{6}b^{-2})^{4}}{(4a^{-3}b^{-3})^{3}}=\dfrac{a^{24}b^{-8}}{64a^{-9}b^{-9}}=...$
Evaluate the division and simplify:
$...=\dfrac{1}{64}a^{24-(-9)}b^{-8-(-9)}=\dfrac{1}{64}a^{33}b=\dfrac{a^{33}b}{64}$