Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I know I have asked a similar question in the past I am stuck on this question.

How would I simplify the following:


I have done

$$\frac{x^3y^{-12}}{2^{-3}x^{-6}}\left(\frac{3^{-1}xy^{-3}}{8x^{-2}\cdot 1}\right)^2$$


Unfortunately I am not sure how to proceed.

share|cite|improve this question
You can find some good starting points on how to format mathematics on the site here and here. This AMS reference is very useful. If you need to format more advanced things, there are many excellent references on LaTeX on the internet, including StackExchange's own TeX.SE site. – Zev Chonoles Jan 16 '13 at 2:37
@ZevChonoles I wish there was a way to +1 an edit. That was awesome, but also a lot of work. Thanks for clearing up the question! – apnorton Jan 16 '13 at 2:42
@anorton: Thanks for your kind words :) I don't want questions to be discriminated against due to poor formatting, and I can write LaTeX pretty quick, so I like to help when I can. – Zev Chonoles Jan 16 '13 at 2:47
up vote 2 down vote accepted

$$\frac{x^9y^{-12}}{2^{-3}}\frac{3^{-2}x^2y^{-6}}{64x^{-4}}$$ Remember that $a^{-n} = \frac{1}{a^n}$. Thus, we have: $$\frac{2^3x^9}{y^{12}}\cdot\frac{x^2x^4}{64\cdot3^2y^6}$$ At this point, we have $a^na^m=a^{n+m}$. I've also changed $64=2^6$. $$\frac{2^3x^{15}}{2^6\cdot3^2y^{18}}$$ Note that we can cancel some of the twos: $$\frac{x^{15}}{2^3\cdot3^2y^{18}}$$ These numbers are easier to work with: $$\frac{x^{15}}{8\cdot9y^{18}}$$ $$\frac{x^{15}}{72y^{18}}$$ Done. :-)

Please let me know if you have any questions. A reminder--please accept the answer that you feel best answers your question (if, in your opinion, one does). This will encourage people to answer your future questions.

share|cite|improve this answer
muchas gracias senor. – Fernando Martinez Jan 17 '13 at 1:43

You're doing well so far! Now you just need to combine the two fractions together, using the rule $$\frac{a}{b}\times\frac{c}{d}=\frac{ac}{bd}$$ Thus, you'll get $$\frac{x^9y^{-12}3^{-2}x^2y^{-6}}{2^{-3}64x^{-4}}$$ I think all the remaining steps after this are ones you've demonstrated knowledge of already, though if you need further help I can add more detail.

share|cite|improve this answer
Thanks for help. – Fernando Martinez Jan 17 '13 at 1:39

Well, the next step would be to get rid of the negative exponents $$\frac{8x^9}{y^{12}}\frac{x^6}{(9)(64)y^6}$$ Now you just simplify by multiplying and reducing the coefficients $$\frac{x^{15}}{72y^{18}}$$ Hope this helps.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.