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