# I need help simplifying this expression...

• March 17th 2008, 12:46 AM
eraser851
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.

• March 17th 2008, 12:48 AM
topher0805
Just to clarify, is this your expression?

$(x^{\frac {1}{4}}\cdot y^{\frac {5}{2}})^{-2}$
• March 17th 2008, 12:49 AM
eraser851
Yes, that's correct.
Sorry, forgot the ^'s before the fractions.
• March 17th 2008, 01:00 AM
topher0805
$
(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 $x^{\frac {1}{2}} = \sqrt {x}$

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