(210/27)^2/3 (54+10/27)^2/3 = (64/27)^2/3 = (4^3/3^3)^2/3 = (4/3)^3×2/3 = (4/3)^2= 4^2/3^2 = 16/9 ...

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Cube Numbers

Simplify: 2...

Question

Simplify: ${(2 \frac{10}{27})}^{\frac{2}{3}}$ .

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Solution

$(2 \frac{10}{27})^{2 / 3}$
$(\frac{54 + 10}{27})^{2 / 3} = (\frac{64}{27})^{2 / 3}$
$= (\frac{4^{3}}{3^{3}})^{2 / 3} = (\frac{4}{3})^{3 \times \frac{2}{3}}$
$= (\frac{4}{3})^{2} = \frac{4^{2}}{3^{2}} = \frac{16}{9}$

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