Evaluate:
(i) (64)^−1/2
(ii) (8)^−1/3
(iii) (81)^−1/4

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Solution

$(i) {(64)}^{\frac{- 1}{2}} = {(8^{2})}^{\frac{- 1}{2}} = 8^{2 \times \frac{- 1}{2}} = 8^{- 1} = \frac{1}{8} (ii) {(8)}^{\frac{- 1}{3}} = {(2^{3})}^{\frac{- 1}{3}} = 2^{3 \times \frac{- 1}{3}} = 2^{- 1} = \frac{1}{2} (iii) {(81)}^{\frac{- 1}{4}} = {(3^{4})}^{\frac{- 1}{4}} = 3^{4 \times \frac{- 1}{4}} = 3^{- 1} = \frac{1}{3}$

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