The value of 4 × (256)^–1/4 ÷ (243)^1/5 is ________.

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Solution

$Let x = 4 \times {(256)}^{- \frac{1}{4}} \div {(243)}^{\frac{1}{5}} \Rightarrow x = 4 \times {(4^{4})}^{- \frac{1}{4}} \div {(3^{5})}^{\frac{1}{5}} \Rightarrow x = 4 \times {(4)}^{4 \times (- \frac{1}{4})} \div {(3)}^{5 \times \frac{1}{5}} \Rightarrow x = 4 \times {(4)}^{- 1} \div {(3)}^{1} \Rightarrow x = 4 \times \frac{1}{4} \div {(3)}^{1} \Rightarrow x = 1 \div 3 \Rightarrow x = \frac{1}{3}$

Hence, the value of 4 × (256)^–1/4 ÷ (243)^1/5 is $\frac{1}{3}$ .

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Similar questions

The value of $\frac{1}{{(216)}^{- \frac{2}{3}}} + \frac{1}{{(256)}^{- \frac{3}{4}}} + \frac{1}{{(32)}^{- \frac{1}{5}}}$ is :

\frac{4}{{(216)}^{\frac{- 2}{3}}} + \frac{1}{{(256)}^{\frac{- 3}{4}}} + \frac{2}{{(243)}^{\frac{- 1}{5}}}

\frac{2}{(216)^{- 2 / 3}} - \frac{4}{(243)^{- \frac{1}{5}}} + \frac{1}{(256)^{- 3 / 4}}

\frac{4}{(216)^{- \frac{2}{3}}} + \frac{1}{(256)^{- \frac{3}{4}}} + \frac{2}{(243)^{- \frac{1}{5}}}

\frac{4}{216^{\frac{- 2}{3}}}

\frac{1}{256^{\frac{- 3}{4}}}

\frac{2}{243^{\frac{- 1}{5}}}

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