Simplify $(243)^{- 0.6}$ using laws of indices

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Solution

The given expression ${(243)}^{- 0.6}$ can be simplified as follows:

${(243)}^{- 0.6} = (3 \times 3 \times 3 \times 3 \times 3)^{- 0.6} = (3^{5})^{- 0.6} = 3^{5 \times - 0.6} (∵ {(x^{m})}^{n} = x^{m \times n})$
$= 3^{- 3} = \frac{1}{3^{3}} (∵ \frac{1}{x^{n}} = x^{- n}) = \frac{1}{27}$

Hence ${(243)}^{- 0.6} = \frac{1}{27}$

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