Question

$\left\{{Question}\right\}$
$Find \: the \: value \: of \: \frac{4}{(216) ^{ - \frac{2}{3} } } + \frac{1}{(256)^{ - \frac{3}{4} } } + \frac{1}{(243)^{ - \frac{1}{5} } }$
Only that user solve question who know this.
Wrong answer will be reported.​

Answer 1

$answer$

214.

Explanation:

Question:

$Find \: the \: value \: of \: \frac{4}{(216) ^{ - \frac{2}{3} } } + \frac{1}{(256)^{ - \frac{3}{4} } } + \frac{1}{(243)^{ - \frac{1}{5} } }$

Solution:

We have,

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

=$\fbox{${{4}{\mathrm{(}}{\mathrm{216}}{\mathrm{)}}^{\frac{2}{3}}\mathrm{{+}}{\mathrm{(}}{\mathrm{256}}{\mathrm{)}}^{\frac{3}{4}}\mathrm{{+}}{2}{\mathrm{(}}{\mathrm{243}}{\mathrm{)}}^{\frac{1}{5}}}$}$

=$\fbox{${{4}{\mathrm{(}}{6}^{3}{\mathrm{)}}^{\frac{2}{3}}\mathrm{{+}}{\mathrm{(}}{4}^{4}{\mathrm{)}}^{\frac{3}{4}}\mathrm{{+}}{2}{\mathrm{(}}{3}^{5}{\mathrm{)}}^{\begin{array}{l}{1}\\{5}\end{array}}}$}$

=$\fbox{${{4}\mathrm{\times}{6}^{3}{}^{\mathrm{\times}}{}^{\frac{2}{3}}\mathrm{{+}}{4}^{4}{}^{\mathrm{\times}}{}^{\frac{3}{4}}\mathrm{{+}}{2}\mathrm{\times}{3}^{5}{}^{\mathrm{\times}}{}^{\frac{1}{5}}}$}$

=$\fbox{${{4}\mathrm{\times}{6}^{2}\mathrm{\times}{4}^{3}\mathrm{{+}}{2}\mathrm{\times}{3}}$}$

=$\fbox{${{\mathrm{144}}\mathrm{{+}}{\mathrm{64}}\mathrm{{+}}{6}}$}$

=$\fbox{${{\mathrm{214}}\hspace{0.33em}{Ans}{\mathrm{.}}}$}$