Question

find value of 4/216 raised to -2/3 - 1/256 raised to -3/4 . no spam answers pls....it will be reported

Answer 1

$Given \: \red{ \Big(\frac{4}{216}\Big)^{\frac{-2}{3}} - \Big(\frac{1}{256}\Big)^{\frac{-3}{4}} }$

$= \Big(\frac{4}{4 \times 54}\Big)^{\frac{-2}{3}} - \Big(\frac{1}{4^4}\Big)^{\frac{-3}{4}}$

$= \Big(\frac{1}{54}\Big)^{\frac{-2}{3}} - \Big(\frac{1}{4}\Big)^{4 \times \frac{-3}{4}}$

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

$= \Big(2\times 3^{3}\Big)^{\frac{2}{3}} - \Big(\frac{1}{4}\Big)^{-3}$

$= 2^{\frac{2}{3}} \times 3^{2} - 4^{3}$

$= (2^{2})^{\frac{1}{3}} \times 3^{2} - 4^{3}$

$= 4^{\frac{1}{3}}\times 9 - 4^{3}$

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