Question

simplify : (√x)^-2/3 √y^4÷√xy^-1/2

Answer 1

$\textbf{Given:}$

$\dfrac{(\sqrt{x})^{\frac{-2}{3}}\sqrt{y^4}}{\sqrt{xy^{\frac{-1}{2}}}}$

$\textbf{To find:}$

$\text{Simplified form of the given expression}$

$\textbf{Solution:}$

$\text{Consider,}$

$\dfrac{(\sqrt{x})^{\frac{-2}{3}}\sqrt{y^4}}{\sqrt{xy^{\frac{-1}{2}}}}$

$=\dfrac{(x^{\frac{1}{2}})^{\frac{-2}{3}}\,y^2}{(xy^{\frac{-1}{2}})^{\frac{1}{2}}}$

$=\dfrac{x^{{\frac{1}{2}}{\times}{\frac{(-2)}{3}}}\,y^2}{x^{\frac{1}{2}}y^{{\frac{-1}{2}}{\times}{\frac{1}{2}}}}$

$=\dfrac{x^{\frac{-1}{3}}\,y^2}{x^{\frac{1}{2}}y^{\frac{-1}{4}}}$

$=x^{\frac{-1}{3}-\frac{1}{2}}\,y^{2+\frac{1}{4}}$

$=x^{\frac{-2-3}{6}}\,y^{\frac{8+1}{4}}$

$=x^{\frac{-5}{6}}\,y^{\frac{9}{4}}$

$\textbf{Answer:}$

$\textbf{The simplified form of the given expression is \bf\,x^{\frac{-5}{6}}\,y^{\frac{9}{4}} }$

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Simplify 73*73*73+27*27*27/73*73-73*27+27*27

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Answer 2

Answer:

1. (x^1/2)^-2/3. (y^4)^1/2/(xy^-1/2)1/2

2. x^-1/3. y^2/x^1/2. y^-1/4.

3. x^-1/3-1/2. y^2+1/4.

4. x^-2-3/6. y^8+1/4.

5. x^-5/6. y^9/4. Ans.