√(y)(2·√(y) √(y^8)) =y^13(2· y^1/3 (y^8)^13) =2· y^13+13 y^13+83 =2y^23 y^3 =2(y^2)^13 y^3 =2√(y^2) y^3 . ...

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Exponential Representation for Irrational Numbers

Solve:- √y2√...

Question

Solve:-
$\sqrt[3]{y} (2 \sqrt[3]{y} - \sqrt[3]{y^{8}})$

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Solution

$\sqrt[3]{y} (2 \cdot \sqrt[3]{y} - \sqrt[3]{y^{8}})$
$= y^{\frac{1}{3}} ⎛ ⎜ ⎝ 2 \cdot y^{1 / 3} - (y^{8})^{\frac{1}{3}} ⎞ ⎟ ⎠$
$= 2 \cdot y^{\frac{1}{3} + \frac{1}{3}} - y^{\frac{1}{3} + \frac{8}{3}}$
$= 2 y^{\frac{2}{3}} - y^{3}$
$= 2 (y^{2})^{\frac{1}{3}} - y^{3}$
$= 2 \sqrt[3]{y^{2}} - y^{3}$ .

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