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The value of given expression is 214.
Step-by-step explanation:
The given expression is
\frac{4}{(216)^{\frac{-2}{3}}}+\frac{1}{(256)^{\frac{-3}{4}}}+\frac{2}{(243)^{\frac{-1}{5}}}
Using exponent property:
x^{\frac{a}{b}}=(x^{\frac{1}{b}})^a
\frac{4}{6^{-2}}+\frac{1}{4^{-3}}+\frac{2}{3^{-1}}
Using exponent property:
\frac{1}{a^{-1}}=a
4\times 6^2+1\times 4^3+2\times 3
4\times 36+1\times 64+2\times 3
144+64+6
214
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