Question

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

`sqrt(x^3y^-2)`

Answer 1

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

Given `sqrt(x^3y^-2)`

As x and y are positive real numbers then we can write

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

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

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

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

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

`=x^(3/2)/y`

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