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