# Simplifying

• Sep 11th 2008, 06:51 PM
johntuan
Simplifying
Sorry for all the questions but i cant seem to figure this one out...

The questions is
[(x^-3)(y^-1)] + y^-5 / [(x^-4)(y5)]

The answer is (xy^4)+(x^4) / y^10
• Sep 11th 2008, 07:06 PM
Shyam
Quote:

Originally Posted by johntuan
Sorry for all the questions but i cant seem to figure this one out...

The questions is
[(x^-3)(y^-1)] + y^-5 / [(x^-4)(y5)]

The answer is (xy^4)+(x^4) / y^10

$\displaystyle x^{-3}y^{-1} + \frac{y^{-5}} {x^{-4}y^5}$

$\displaystyle xy^4 + \frac{x^4}{y^{10}}$ or it is $\displaystyle \frac{xy^4 + x^4}{y^{10}}$
• Sep 11th 2008, 07:10 PM
johntuan
Quote:

Originally Posted by Shyam

$\displaystyle x^{-3}y^{-1} + \frac{y^{-5}} {x^{-4}y^5}$

$\displaystyle xy^4 + \frac{x^4}{y^{10}}$ or it is $\displaystyle \frac{xy^4 + x^4}{y^{10}}$

for the question its
[(x^-3)(y^-1)] + y^-5] / [(x^-4)(y5)], so basically its all over [(x^-4)(y5)].

and for the answer its the second one...sorry for the mixup.
• Sep 11th 2008, 07:21 PM
Shyam
Quote:

Originally Posted by johntuan
Sorry for all the questions but i cant seem to figure this one out...

The questions is
[(x^-3)(y^-1)] + y^-5 / [(x^-4)(y5)]

The answer is (xy^4)+(x^4) / y^10

$\displaystyle =\frac{x^{-3}y^{-1}+y^{-5}}{x^{-4}y^5}$

$\displaystyle =\frac{\frac{1}{x^3y}+\frac{1}{y^5}}{x^{-4}y^5}$

$\displaystyle =\left(\frac{1}{x^3y}+\frac{1}{y^5}\right)\div ({x^{-4}y^5})$

$\displaystyle = \left(\frac {y^5+x^3y}{x^3y^6}\right)\times \frac{1}{x^{-4}y^5}$

$\displaystyle = \frac {y(y^4+x^3)}{x^3y^6}\times \frac{x^4}{y^5}$

$\displaystyle = \frac {y^4+x^3}{y^5}\times \frac{x}{y^5}$

$\displaystyle = \frac {xy^4+x^4}{y^{10}}$

Did you get it NOW ???
• Sep 11th 2008, 07:25 PM
johntuan
Quote:

Originally Posted by Shyam
$\displaystyle =\frac{x^{-3}y^{-1}+y^{-5}}{x^{-4}y^5}$

$\displaystyle =\frac{\frac{1}{x^3y}+\frac{1}{y^5}}{x^{-4}y^5}$

$\displaystyle =\frac{\frac{1}{x^3y}+\frac{1}{y^5}}{x^{-4}y^5}$

$\displaystyle = \frac {y^4+x^3}{x^3y^5}\times \frac{x^4}{y^5}$

$\displaystyle = \frac {y^4+x^3}{y^5}\times \frac{x}{y^5}$

$\displaystyle = \frac {xy^4+x^4}{y^{10}}$

i'm still a bit confused how did u get from the 3rd step to the 4th?
• Sep 11th 2008, 07:59 PM
Shyam
$\displaystyle =\frac{\frac{1}{x^3y}+\frac{1}{y^5}}{x^{-4}y^5}$

$\displaystyle =\left(\frac{1}{x^3y}+\frac{1}{y^5}\right)\div ({x^{-4}y^5})$

(inside the brackets, for numerators, multiply the Numerator of first with Denominator of second, multiply the Numerator of second with Denominator of first), (and for denominator, multiply both the denominators)

$\displaystyle = \left(\frac {1\times y^5+x^3y\times 1}{x^3y \times y^5}\right)\times \frac{1}{x^{-4}y^5}$

$\displaystyle = \left(\frac {y^5+x^3y}{x^3y^6}\right)\times \frac{1}{x^{-4}y^5}$

(take y common from numerator)

$\displaystyle = \frac {y(y^4+x^3)}{x^3y^6}\times \frac{x^4}{y^5}$

$\displaystyle = \frac {y^4+x^3}{y^5}\times \frac{x}{y^5}$

$\displaystyle = \frac {xy^4+x^4}{y^{10}}$

Do you know how to add fractions ??? did you get it now??