Simplyfy (√x)⅔√y⁴÷√xy-½ is
Answers
your answer is here buddy.....
Given:
\dfrac{(\sqrt{x})^{\frac{-2}{3}}\sqrt{y^4}}{\sqrt{xy^{\frac{-1}{2}}}}
xy
2
−1
(
x
)
3
−2
y
4
\textbf{To find:}To find:
\text{Simplified form of the given expression}Simplified form of the given expression
\textbf{Solution:}Solution:
\text{Consider,}Consider,
\dfrac{(\sqrt{x})^{\frac{-2}{3}}\sqrt{y^4}}{\sqrt{xy^{\frac{-1}{2}}}}
xy
2
−1
(
x
)
3
−2
y
4
=\dfrac{(x^{\frac{1}{2}})^{\frac{-2}{3}}\,y^2}{(xy^{\frac{-1}{2}})^{\frac{1}{2}}}=
(xy
2
−1
)
2
1
(x
2
1
)
3
−2
y
2
=\dfrac{x^{{\frac{1}{2}}{\times}{\frac{(-2)}{3}}}\,y^2}{x^{\frac{1}{2}}y^{{\frac{-1}{2}}{\times}{\frac{1}{2}}}}=
x
2
1
y
2
−1
×
2
1
x
2
1
×
3
(−2)
y
2
=\dfrac{x^{\frac{-1}{3}}\,y^2}{x^{\frac{1}{2}}y^{\frac{-1}{4}}}=
x
2
1
y
4
−1
x
3
−1
y
2
=x^{\frac{-1}{3}-\frac{1}{2}}\,y^{2+\frac{1}{4}}=x
3
−1
−
2
1
y
2+
4
1
=x^{\frac{-2-3}{6}}\,y^{\frac{8+1}{4}}=x
6
−2−3
y
4
8+1
=x^{\frac{-5}{6}}\,y^{\frac{9}{4}}=x
6
−5
y
4
9
\textbf{Answer:}Answer:
\textbf{The simplified form of the given expression is $\bf\,x^{\frac{-5}{6}}\,y^{\frac{9}{4}}$}The simplified form of the given question