Simplify algebra exponent I know I have asked a similar question in the past I am stuck on this question.
How would I simplify the following:
$$\left(\frac{xy^{-4}}{2^{-1}x^{-2}}\right)^3\left(\frac{8x^{-2}y^0}{3^{-1}xy^{-3}}\right)^{-2}$$
I have done
$$\frac{x^3y^{-12}}{2^{-3}x^{-6}}\left(\frac{3^{-1}xy^{-3}}{8x^{-2}\cdot 1}\right)^2$$
$$\frac{x^9y^{-12}}{2^{-3}}\frac{3^{-2}x^2y^{-6}}{64x^{-4}}$$
Unfortunately I am not sure how to proceed.  
 A: 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.
A: $$\frac{x^9y^{-12}}{2^{-3}}\frac{3^{-2}x^2y^{-6}}{64x^{-4}}$$
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.
A: 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.
