Applications of the Laws of Indices

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Simplify $\frac{ (p^{13} q^{-3} r^{-18})^{3} }{ (p^{-1} q^{19} r^{-11})^{9} } $

**Answer**

$\;\;\; \frac{ (p^{13} q^{-3} r^{-18})^{3} }{ (p^{-1} q^{19} r^{-11})^{9} } $

$=\frac{p^{39} q^{-9} r^{-54}}{p^{-9} q^{171} r^{-99}} $

$=\frac{p^{39}p^{9}r^{99}}{q^{9}q^{171}r^{54}}$

$=\frac{p^{48}r^{45}}{q^{180}}$