Solving Exponent Laws: (p^2q+ pq^3)^3 / p^3q^4

[majinknight]

Hi, i am having a little trouble with a couple of math questions, i thought i was doing them right but cannot get the answer. Ok the questions are:

(p^2q+ pq^3)^3 / p^3q^4

Now I do not know what to do, the answer i was told is suppose to be:

(p+q^2)^3 / q

I just don't know how to get that, if someone could walk me through this one question it would be appreciated.

 

[Janus]

you start with:

\frac{(p^2q+pq^3)^3}{p^3q^4}

Factor out pq in the numerator:

\frac{(pq(p+q^2))^3}{p^3q^4}

same as:

\frac{(pq)^3(p+q^2)^3}{p^3q^4}

\frac{p^3q^3(p+q^2)^3}{p^3q^4}

apply division rule for exponents:

\frac{(p+q^2)^3}{q}

 

[majinknight]

Oh my god, thank you, i completely understand know. I had sort of done what you had but instead did not factor and so it just kept getting more complicated and confusing me. Thank you so much.

 

[Pyrrhus]

What did you do? expand it?, if you had you will get the same just with the numerador expanded, but it will be more work.