Example Question - solving fractions with exponents

Simplification of a Fraction with Exponents

\[ \left( \frac{4a^6b^5c^{-2}}{(2a^{-4}b^6c)^3} \right)^{-1} = \left( \frac{4a^6c^{-2}}{2^3a^{-12}b^{18}c^3} \right)^{-1} = \left( \frac{4a^{18}c^{-2}}{8b^{18}c^3} \right)^{-1} = \left( \frac{a^{18}c^{-2}}{2b^{18}c^3} \right)^{-1} = \frac{2b^{18}c^3}{a^{18}c^{-2}} \] \[ = 2b^{18}c^{3}a^{-18}c^{2} = 2b^{18}a^{-18}c^{5} \]