Applications of the Laws of Indices

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Simplify $\frac{ (p^{-19} q^{17} r^{13})^{-4} }{ (p^{-12} q^{-14} r^{-6})^{-1} } $

**Answer**

$\;\;\; \frac{ (p^{-19} q^{17} r^{13})^{-4} }{ (p^{-12} q^{-14} r^{-6})^{-1} } $

$=\frac{p^{76} q^{-68} r^{-52}}{p^{12} q^{14} r^{6}} $

$=\frac{p^{76}}{p^{12}q^{68}q^{14}r^{52}r^{6}}$

$=\frac{p^{64}}{q^{82}r^{58}}$