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.

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- Mar 16th 2008, 11:46 PMeraser851I 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. - Mar 16th 2008, 11:48 PMtopher0805
Just to clarify, is this your expression?

$\displaystyle (x^{\frac {1}{4}}\cdot y^{\frac {5}{2}})^{-2}$ - Mar 16th 2008, 11:49 PMeraser851
Yes, that's correct.

Sorry, forgot the ^'s before the fractions. - Mar 17th 2008, 12:00 AMtopher0805
$\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 $\displaystyle x^{\frac {1}{2}} = \sqrt {x}$

So your final expression is:

$\displaystyle \frac {1}{\sqrt {x}\cdot y^5}$ - Mar 17th 2008, 12:01 AMeraser851
Oh wow, thank you so much.

I'll record that into my notes!