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12 × 4^-3 × a^-5 / 27 × a^-4

\frac{12 \times 4^{- 3} \times a^{- 5}}{27 \times a^{- 4}} [a^{- m} = \frac{1}{a^{m}}] = \frac{12 \times \frac{1}{4^{3}} \times \frac{1}{a^{5}}}{27 \times \frac{1}{a^{4}}} = \frac{4 \times 3 \times \frac{1}{4^{3}} \times \frac{1}{a^{5}} \times a^{4}}{27} = \frac{4 \times 3 \times \frac{1}{4^{3}} \times \frac{1}{a^{5}} \times a^{4}}{3^{3}} [\frac{a^{m}}{a^{m - n}} = a^{m - n}] \frac{3 \times \frac{4}{4^{3}} \times \frac{a^{4}}{a^{5}}}{3^{3}} = \frac{3}{3^{3}} \times \frac{4}{4^{3}} \times \frac{a^{4}}{a^{5}} = 3^{1 - 3} \times 4^{1 - 3} \times a^{4 - 5} = 3^{- 2} \times 4^{- 2} \times a^{- 1} [a^{m} b^{m} = {(a b)}^{m}] = {(3 \times 4)}^{- 2} \times a^{- 1} = 12^{- 2} \times a^{- 1}

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