Applications of the Laws of Indices

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Simplify $\frac{ (k^{4} l^{-15} m^{-2})^{-18} }{ (k^{14} l^{7} m^{15})^{4} } $

**Answer**

$\;\;\; \frac{ (k^{4} l^{-15} m^{-2})^{-18} }{ (k^{14} l^{7} m^{15})^{4} } $

$=\frac{k^{-72} l^{270} m^{36}}{k^{56} l^{28} m^{60}} $

$=\frac{l^{270}m^{36}}{k^{72}k^{56}l^{28}m^{60}}$

$=\frac{l^{242}}{k^{128}m^{24}}$