Answer
$\dfrac{b^{20}}{a^{15}}$
Work Step by Step
Use the rule $(\frac{a}{b})^{-m}=(\frac{b}{a})^m$ to obtain:
$\left(\dfrac{a^3}{b^4}\right)^{-5}=\left(\dfrac{b^4}{a^3}\right)^5$
Use the rule $(a^m)^n=a^{mn}$ to obtain:
$\left(\dfrac{b^4}{a^3}\right)^5=\dfrac{b^{4(5)}}{a^{3(5)}}=\dfrac{b^{20}}{a^{15}}$
