Evaluate:
(i) (25)^3/2
(ii) (32)^2/5
(iii) (81)^3/4

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Solution

$(i) {(25)}^{\frac{3}{2}} = 5^{2 \times \frac{3}{2}} = 5^{3} = 125 [(a^{m})^{n} = a^{m n}] (ii) {(32)}^{\frac{2}{5}} = {(2^{5})}^{\frac{2}{5}} = 2^{5 \times \frac{2}{5}} = 2^{2} = 4 (iii) {(81)}^{\frac{3}{4}} = {(3^{4})}^{\frac{3}{4}} = 3^{4 \times \frac{3}{4}} = 3^{3} = 27$

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