Simplify $(xy^{-1})/(y^2/x^3)^{-1}$

Question

Need to simplify this equation:

$$(xy^{-1})/(y^2/x^3)^{-1}$$

So far I have

$= \frac{x/y}{1/(y^2/x^3)}$

But don't know what to do next. Any help much appreciated

Can you explain how you got there? Just so that we know what techniques you are (and aren't) familiar with. — rurouniwallace, Aug 02 '13 at 13:19

score 3 · Accepted Answer · answered Aug 02 '13 at 13:31

3

We have $$(xy^{-1})/(y^2/x^3)^{-1}=(xy^{-1})\times\left(\frac{y^2}{x^3}\right)^{+1}=\frac{x}{y}\times\frac{y^2}{x^3}=\frac{y}{x^2}$$ provided $$x\ne0, y\ne0$$

answered Aug 02 '13 at 13:31

Mikasa

67,374

;-) $+^++^++^++$ – amWhy Aug 02 '13 at 22:14
@amWhy: It is very kind of you considering my small attempts here. Thank you. :) – Mikasa Aug 02 '13 at 22:21

score 2 · Answer 2 · answered Aug 02 '13 at 13:19

2

Hint: Use $x^a x^b = x^{a+b}$ and $1/x^a = x^{-a}$ to simplify equation to form something like $x^a y^b$.

answered Aug 02 '13 at 13:19

JiminP

1,670

Simplify $(xy^{-1})/(y^2/x^3)^{-1}$

2 Answers2