Answer
$\dfrac{(a^{4}b^{-7})^{-5}}{(5a^{2}b^{-1})^{-2}}=\dfrac{25b^{33}}{a^{16}}$
Work Step by Step
$\dfrac{(a^{4}b^{-7})^{-5}}{(5a^{2}b^{-1})^{-2}}$
Evaluate the exponential expressions in the numerator and the denominator:
$\dfrac{(a^{4}b^{-7})^{-5}}{(5a^{2}b^{-1})^{-2}}=\dfrac{a^{-20}b^{35}}{(5)^{-2}a^{-4}b^{2}}=...$
Evaluate the division and simplify:
$...=5^{2}a^{-20-(-4)}b^{35-2}=25a^{-16}b^{33}=\dfrac{25b^{33}}{a^{16}}$