Question
Evaluate:
$\frac{4}{(216)^{-\frac{2}{3}}}+\frac{1}{(256)^{-\frac{3}{4}}}+\frac{2}{(243)^{-\frac{1}{5}}}$
$\frac{4}{(216)^{-\frac{2}{3}}}+\frac{1}{(256)^{-\frac{3}{4}}}+\frac{2}{(243)^{-\frac{1}{5}}}$
✓
Answer
$\frac{4}{(216)^{-\frac{2}{3}}}+\frac{1}{(256)^{-\frac{3}{4}}}+\frac{2}{(243)^{-\frac{1}{5}}}$
$=\frac{4}{(6^3)^{-\frac{2}{3}}}+\frac{1}{(4^4)^{-\frac{3}{4}}}+\frac{2}{(3^5)^{-\frac{1}{5}}}$
$=\frac{4}{6^{3\times\big(-\frac{2}{3}\big)}}+\frac{1}{4^{4\times\big(-\frac{3}{4}\big)}}+\frac{2}{3^{5\times\big(-\frac{1}{5}\big)}}$
$=\frac{4}{6^{-2}}+\frac{1}{4^{-3}}+\frac{2}{3^{-1}}$
$=4\times6^2+1\times4^3+2\times3$
$=4\times36+64+6$
$=144+70$
$=214$
$=\frac{4}{(6^3)^{-\frac{2}{3}}}+\frac{1}{(4^4)^{-\frac{3}{4}}}+\frac{2}{(3^5)^{-\frac{1}{5}}}$
$=\frac{4}{6^{3\times\big(-\frac{2}{3}\big)}}+\frac{1}{4^{4\times\big(-\frac{3}{4}\big)}}+\frac{2}{3^{5\times\big(-\frac{1}{5}\big)}}$
$=\frac{4}{6^{-2}}+\frac{1}{4^{-3}}+\frac{2}{3^{-1}}$
$=4\times6^2+1\times4^3+2\times3$
$=4\times36+64+6$
$=144+70$
$=214$
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