simplify

euclid2 · #1 $Old$ December 4th, 2008, 04:10 PM

$(x^2y)^-2 \frac {{(xy^3)}}{{(x^2y^2)}}^2$

Sorry it's not very clear
(x^2y)^-2 (xy^3/x^2y^2)^2

euclid2 · #2 $Old$ December 4th, 2008, 04:22 PM

Quote:

Originally Posted by nzmathman $View Post$

$x^2y - 2 \frac{(xy^3)^2}{x^2 y^2}$

Square the top part of fraction:

$= x^2y - 2\frac{x^2 y^6}{x^2 y^2}$

Cancel the $x^2$ and the $y^2$ on the bottom:

$= x^2y - 2y^4$

Simplify fully, factorise:

$= y(x^2 - 2y^3)$

the first part is to the power of -2, and for the second part the power of 2 applied to the numerator and denominator, sorry

nzmathman · #3 $Old$ December 4th, 2008, 04:31 PM

Yes I deleted that message and will have a go again for you.

$(x^2 y)^{-2} \times \left( \frac{xy^3}{x^2 y^2} \right)^2$

Simplify the second fraction (cancel a common factor of $xy^2$ )

$= \frac{1}{(x^2y)^2} \times \left( \frac{y}{x} \right)^2$

$= \frac{1}{x^4 y^2} \times \frac{y^2}{x^2}$

Cancel the common factor of $y^2$

$= \frac{1}{x^4} \times \frac{1}{x^2}$

$= \frac{1}{x^6} = x^{-6}$

euclid2 · #4 $Old$ December 4th, 2008, 04:34 PM

Quote:

Originally Posted by nzmathman $View Post$

Yes I deleted that message and will have a go again for you.

$(x^2 y)^{-2} \times \left( \frac{xy^3}{x^2 y^2} \right)^2$

Simplify the second fraction (cancel a common factor of $xy^2$ )

$= \frac{1}{(x^2y)^2} \times \left( \frac{y}{x} \right)^2$

$= \frac{1}{x^4 y^2} \times \frac{y^2}{x^2}$

Cancel the common factor of $y^2$

$= \frac{1}{x^4} \times \frac{1}{x^2}$

$= \frac{1}{x^6} = x^{-6}$

That's better, thanks.