Question

(√x)-2/3 √y4.÷ √xy-1/2​

Answer 1

Answer:

x^{-\frac{5}{6}}.y^{\frac{7}{4}}

Step-by-step explanation:

Here, the given expression is,

\frac{(\sqrt{x})^{-\frac{2}{3}}.\sqrt{y^4}}{\sqrt{x.y^{-1/2}} }

=\frac{(x^{\frac{1}{2}})^{-\frac{2}{3}}\times (y^\frac{1}{2})^4}{x^\frac{1}{2}\times (y^\frac{1}{2})^{-\frac{1}{2}}}

=\frac{x^{\frac{1}{2}\times \frac{-2}{3}}.y^{\frac{1}{2}\times 4}}{x^\frac{1}{2}\times y^{\frac{1}{2}\times -\frac{1}{2}}}

=\frac{x^{-\frac{1}{3}}\times y^2}{x^\frac{1}{2}\times y^{-\frac{1}{4}}}

(\text{ Since, } (a^m)^n=a^{m\times n)

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

(\text{ Since, }\frac{a^m}{a^n}=a^{m-n})

=x^{-\frac{5}{6}}.y^{\frac{7}{4}}