# 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
Write your answer without using negative exponents.
Assume that all variables are positive real numbers.

Thank you in advance.

2. Just to clarify, is this your expression?

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

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

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

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

$
x^{-2}$

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

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

Using this rule, we can say that:

$
(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:

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

So we can simplify our expression to:

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

Simplify the fractions:

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

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

So your final expression is:

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

5. Oh wow, thank you so much.
I'll record that into my notes!