X=2√3 y=4√5 find the x+y and x-y
Answers
Answer:
(
x
)
3
−2
4
÷
xy
2
−1
=(x
2
1
)
3
−2
(y
4
)
2
1
÷(xy
2
−1
)
2
1
=x
3
−1
y
2
÷x
2
1
y
4
−1
since (a
m
)
n
=a
mn
=
x
2
1
y
4
−1
x
3
−1
y
2
=x
3
−1
+
2
1
y
2+
4
1
since a
−m
=
a
m
1
=x
6
−2+3
y
4
9
=x
6
1
y
4
9
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Step-by-step explanation:
\textbf{Given:}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 expression is x
6
−5
y
4
9
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