# Thread: I need help simplifying this expression...

1. ## I need help simplifying this expression...

Could somebody please explain how to simplify this expression?
(x1/4*y5/2)^-2
Assume that all variables are positive real numbers.

2. Just to clarify, is this your expression?

$\displaystyle (x^{\frac {1}{4}}\cdot y^{\frac {5}{2}})^{-2}$

3. Yes, that's correct.
Sorry, forgot the ^'s before the fractions.

4. $\displaystyle (x^{\frac {1}{4}}\cdot y^{\frac {5}{2}})^{-2}$

Recall that when you raise a variable to a negative exponent like this:

$\displaystyle x^{-2}$

You can change the sign of the exponent by dividing the variable into 1. So:

$\displaystyle x^{-2} = \frac {1}{x^2}$

Using this rule, we can say that:

$\displaystyle (x^{\frac {1}{4}}\cdot y^{\frac {5}{2}})^{-2} = \frac {1}{(x^{\frac {1}{4}}\cdot y^{\frac {5}{2}})^{2}}$

Recall the rule of exponents that says:

$\displaystyle (x^a)^b = x^{ab}$

So we can simplify our expression to:

$\displaystyle \frac {1}{(x^{\frac {2}{4}}\cdot y^{\frac {10}{2}})}$

Simplify the fractions:

$\displaystyle \frac {1}{(x^{\frac {1}{2}}\cdot y^5)}$

And recall that $\displaystyle x^{\frac {1}{2}} = \sqrt {x}$

$\displaystyle \frac {1}{\sqrt {x}\cdot y^5}$