 # If x^{2} =y^{3} and y>1, what does x^frac{2}{3} equal in terms of y? smileycellist2 2021-01-19 Answered
If ${x}^{2}={y}^{3}$ and y>1, what does ${x}^{\frac{2}{3}}$ equal in terms of y?
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${\left(X\right)}^{\frac{2}{3}}={\left({X}^{2}\right)}^{\frac{1}{3}}-------------r\underset{―}{e}$
$\left(X{\right)}^{\frac{m}{n}}=\left(X{\right)}^{m\frac{1}{n}}$
compensate by $\left(X{\right)}^{2}=\left(Y{\right)}^{3}$
${\left(X\right)}^{\frac{2}{3}}={\left({Y}^{3}\right)}^{\frac{1}{3}}={\left(Y\right)}^{3}×\frac{1}{3}=Y$
thus
${\left(X\right)}^{\frac{2}{3}}=Y$
${\left(X\right)}^{2}={\left(Y\right)}^{3}$ ------------ take the cube root of both sides
${\left({X}^{2}\right)}^{\frac{1}{3}}={\left({\left(Y\right)}^{3}\right)}^{\frac{1}{3}}$
$\left({X}^{2×\frac{1}{3}}={Y}^{3}×\frac{1}{3}$
${\left(X\right)}^{\frac{2}{3}}=Y$
answer ------------- ${\left(X\right)}^{\frac{2}{3}}=Y$

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