Answer
$\displaystyle \frac{b}{a^{3}}$
Work Step by Step
$[\displaystyle \frac{a^{-7}b^{-1}}{b^{-4}a^{2}}]^{1/3}$ =...... use: $\displaystyle \frac{a^{m}}{a^{n}}=a^{m-n}$
=$[a^{-7-2}b^{-1-(-4)}]^{1/3}$
$=(a^{-9}b^{3})^{1/3}$ =...... use: $(ab)^{m}=a^{m}b^{m}$
$=(a^{-9})^{1/3}(b^{3})^{1/3}$ =...... use: $(a^{m})^{n}=a^{mn}$
$=a^{-3}b^{1}$ =......use: $\displaystyle \frac{1}{a^{n}}=a^{-n}$
$= \displaystyle \frac{b}{a^{3}}$
