# How do you write #y^(-1/2)/x^(1/2)# in radical form?

##### 1 Answer

#### Explanation:

Your starting expression looks like this

#y^(-1/2)/x^(1/2)#

The first thing to do is rewrite the *negative exponent* as a positive exponent. You know that

#color(blue)(n^(-a) = 1/n^a)#

In your case, you have

#y^(-1/2) = 1/y^(1/2)#

The expression becomes

#y^(-1/2)/x^(1/2) = 1/x^(1/2) * 1/y^(1/2)#

Take a look at the denominator. You have

#x^(1/2) * y^(1/2) = (x * y)^(1/2)#

The expression is now equaivalent to

#1/x^(1/2) * 1/y^(1/2) = 1^(1/2)/(x * y)^(1/2) = (1/(x * y))^(1/2)#

You know that

#color(blue)( n^(a/b) = root(b)(n^a))#

In your case, you will have

#(1/(xy))^(1/2) = sqrt(1/(xy))#

**Extra step**

You can rationalize the denominator and simplify this expression further

#sqrt(1/(xy)) = sqrt(1)/sqrt(xy) = 1/sqrt(xy) * sqrt(xy)/sqrt(xy) = sqrt(xy)/(sqrt(xy) * sqrt(xy)) = sqrt(xy)/(xy)#