Evaluate: (64 125 )^ -2 3 + (256 625 )^ -1 4 + (3 7 )^0 - Vidyadip

Question

Evaluate:
$\Big(\frac{64}{125}\Big)^{-\frac{2}{3}}+\Big(\frac{256}{625}\Big)^{-\frac{1}{4}}+\Big(\frac{3}{7}\Big)^0$

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Answer

$\Big(\frac{64}{125}\Big)^{-\frac{2}{3}}+\Big(\frac{256}{625}\Big)^{-\frac{1}{4}}+\Big(\frac{3}{7}\Big)^0$
$\Big(\frac{125}{64}\Big)^{\frac{2}{3}}+\Big(\frac{625}{256}\Big)^{\frac{1}{4}}+1$
$=\Big(\frac{5^3}{4^3}\Big)^{\frac{2}{3}}+\Big(\frac{5^4}{4^4}\Big)^{\frac{1}{4}}+1$
$=\frac{5^{3\times\frac{2}{3}}}{4^{3\times\frac{2}{3}}}+\frac{5^{4\times\frac{1}{4}}}{4^{4\times\frac{1}{4}}}+1$
$=\frac{5^2}{4^2}+\frac{5}{4}+1$
$=\frac{25}{16}+\frac{5}{4}+1$
$=\frac{25+20+16}{16}$
$=\frac{61}{16}$

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