81^1/4 × 9^3/2 × 27^–4/3 is equal to _________.

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Solution

$81^{\frac{1}{4}} \times 9^{\frac{3}{2}} \times 27^{- \frac{4}{3}} = {(3^{4})}^{\frac{1}{4}} \times {(3^{2})}^{\frac{3}{2}} \times \frac{1}{27^{\frac{4}{3}}} = {(3)}^{4 \times \frac{1}{4}} \times {(3)}^{2 \times \frac{3}{2}} \times \frac{1}{{(3^{3})}^{\frac{4}{3}}} = {(3)}^{1} \times {(3)}^{3} \times \frac{1}{{(3)}^{3 \times \frac{4}{3}}} = {(3)}^{1 + 3} \times \frac{1}{3^{4}} = {(3)}^{4} \times \frac{1}{3^{4}} = 1$

Hence, 81^1/4 × 9^3/2 × 27^–4/3 is equal to 1.

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