Question

Assuming that x, y, z are positive real numbers, simplify the following:

`(x^((-2)/3)y^((-1)/2))^2`

Answer 1

We have to simplify the following, assuming that x, y, z are positive real numbers

Given `(x^((-2)/3)y^((-1)/2))^2`

As x and y are positive real numbers then we have

`(x^((-2)/3)y^((-1)/2))^2=(x^((-2)/3)xxx^((-2)/3)xxy^((-1)/2)xxy^((-1)/2))`

By using law of rational exponents `a^-n=1/a^n` we have

`(x^((-2)/3)y^((-1)/2))^2=1/x^(2/3)xx1/x^(2/3)xx1/y^(1/2)xx1/y^(1/2)`

`(x^((-2)/3)y^((-1)/2))^2=1/(x^(2/3)xx x^(2/3))xx1/(y^(1/2)xxy^(1/2))`

By using law of rational exponents `a^m xx a^n=a^(m+n)` we have

`(x^((-2)/3)y^((-1)/2))^2=1/x^(2/3+2/3)xx1/y^(1/2+1/2)`

`=1/x^(4/3)xx1/y^(2/2)`

`=1/x^(4/3)xx1/y`

`=1/(x^(4/3)y)`

Hence the simplified value of `(x^((-2)/3)y^((-1)/2))^2` is `1/(x^(4/3)y)`