Evaluate the following :(64/125)^(-2/3) ÷ 1/[256/625]^1/4 + [√25/∛64]^0

Given, Simplifying the expression : Hence, .

Mathematics

Evaluate the following :
$\Big(\dfrac{64}{125}\Big)^{-\dfrac{2}{3}} ÷ \dfrac{1}{\Big(\dfrac{256}{625}\Big)^{\dfrac{1}{4}}} + \Big(\dfrac{\sqrt{25}}{\sqrt[3]{64}}\Big)^0$

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Given,

$\Big(\dfrac{64}{125}\Big)^{-\dfrac{2}{3}} ÷ \dfrac{1}{\Big(\dfrac{256}{625}\Big)^{\dfrac{1}{4}}} + \Big(\dfrac{\sqrt{25}}{\sqrt[3]{64}}\Big)^0$

Simplifying the expression :

$\Rightarrow \Big(\dfrac{64}{125}\Big)^{-\dfrac{2}{3}} ÷ \dfrac{1}{\Big(\dfrac{256}{625}\Big)^{\dfrac{1}{4}}} + \Big(\dfrac{\sqrt{25}}{\sqrt[3]{64}}\Big)^0 \\[1em] \Rightarrow \Big(\dfrac{125}{64}\Big)^{\dfrac{2}{3}} ÷ \dfrac{1}{\Big(\dfrac{4^4}{5^4}\Big)^{\dfrac{1}{4}}} + 1 \\[1em] \Rightarrow \Big(\dfrac{5^3}{4^3}\Big)^{\dfrac{2}{3}} ÷ \dfrac{1}{\Big(\dfrac{4}{5}\Big)^{4 \times \dfrac{1}{4}}} + 1 \\[1em] \Rightarrow \Big(\dfrac{5}{4}\Big)^{3 \times \dfrac{2}{3}} ÷ \dfrac{1}{\Big(\dfrac{4}{5}\Big)} + 1 \\[1em] \Rightarrow \Big(\dfrac{5}{4}\Big)^2 ÷ \dfrac{5}{4} + 1 \\[1em] \Rightarrow \dfrac{25}{16} ÷ \dfrac{5}{4} + 1 \\[1em] \Rightarrow \dfrac{25}{16} \times \dfrac{4}{5} + 1 \\[1em] \Rightarrow \dfrac{5}{4} + 1 \\[1em] \Rightarrow \dfrac{5 + 4}{4} \\[1em] \Rightarrow \dfrac{9}{4} \\[1em] \Rightarrow 2\dfrac{1}{4}.$

Hence, $\Big(\dfrac{64}{125}\Big)^{-\dfrac{2}{3}} ÷ \dfrac{1}{\Big(\dfrac{256}{625}\Big)^{\dfrac{1}{4}}} + \Big(\dfrac{\sqrt{25}}{\sqrt[3]{64}}\Big)^0 = 2\dfrac{1}{4}$ .

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Mathematics

Evaluate the following :
$\Big(\dfrac{64}{125}\Big)^{-\dfrac{2}{3}} ÷ \dfrac{1}{\Big(\dfrac{256}{625}\Big)^{\dfrac{1}{4}}} + \Big(\dfrac{\sqrt{25}}{\sqrt[3]{64}}\Big)^0$

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$\Big(\dfrac{16}{81}\Big)^{-\dfrac{3}{4}} \times \Big(\dfrac{49}{9}\Big)^{\dfrac{3}{2}} ÷ \Big(\dfrac{343}{216}\Big)^{\dfrac{2}{3}}$

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