How do I simplify ((x^2)/(4y^-2))^(-1/2)(x24y2)12?

2 Answers

2/{xy}2xy

Explanation:

(x^2/{4y^{-2}})^{-1/2}(x24y2)12

=({x^2y^2}/{4})^{-1/2}=(x2y24)12

=({(xy)^2}/{4})^{-1/2}=((xy)24)12

={((xy)^2)^{-1/2}}/{4^{-1/2}}=((xy)2)12412

=4^{1/2}(xy)^{2(-1/2)}=412(xy)2(12)

=(2^2)^{1/2}(xy)^{-1}=(22)12(xy)1

=\frac{2^{2(1/2)}}{xy}=22(12)xy

=2/{xy}=2xy

Jul 26, 2018

(x^2/(4y^(-2)))^(-1/2)=2/(xy)(x24y2)12=2xy

Explanation:

Let ,

A=(x^2/(4y^(-2)))^(-1/2)A=(x24y2)12

:.A=(x^2)^(-1/2)/((4y^(-2))^(-1/2)).....to[because(a/b)^n=a^n/b^n]

:.A=x^(2xx(-1/2))/(4^(-1/2)*y^((-2)(-1/2)))to[because(a^m)^n=a^(mn),(ab)^n=a^n*b^n]

:.A=x^(-1)/((2^2)^(-1/2)y^1

:.A=(1/x)/(2^-1 y)

:.A=2^1 xx 1/(xy)

:.A=2/(xy)