Simplify $\left(\dfrac{2p^3}{5q}\right)^{-2}\times\dfrac{4}{p^{-7}q^{-4}}$, leaving your answer in positive indices. Ans: ___

1. Apply the negative index to the fraction and simplify the second fraction with negative indices.

$\left(\frac{2p^3}{5q}\right)^{-2}=\left(\frac{5q}{2p^3}\right)^2=\frac{25q^2}{4p^6}$

$\frac{4}{p^{-7}q^{-4}}=4p^7q^4$

2. Multiply the simplified expressions and combine like bases.

$\frac{25q^2}{4p^6}\times 4p^7q^4$

$=25p^{7-6}q^{2+4}$

$=25pq^6$