remember that (ab)/(cd)=(a/c)(b/c)
also remember that [tex](a^b)^c=a^{bc}=(a^c)^b[/tex]
also, [tex]\frac{a^b}{a^c}=a^{b-c}[/tex] and [tex]a^{-b}=\frac{1}{a^b}[/tex] and [tex](ab)^c=(a^c)(b^c)[/tex]
group the like bits together
[tex]\frac{3(2x^4y^6)^5}{(3x^6y^3)^4}=[/tex]
[tex]\frac{3(2^5)((x^4)^5)((y^6)^5)}{(3^4)((x^6)^4)((y^3)^4)}=[/tex]
[tex]\frac{(3^1)(2^5)(x^{20})(y^{30})}{(3^4)(x^{24})(y^{12})}=[/tex]
[tex](\frac{3^1}{3^4})(\frac{2^5}{1})(\frac{x^{20}}{x^{24}})(\frac{y^{30}}{y^{12}})=[/tex]
[tex](3^{1-4})(2^5)(x^{20-24})(y^{30-12})=[/tex]
[tex](3^{-3})(2^5)(x^{-4})(y^{18})=[/tex]
[tex](\frac{1}{3^3})(\frac{2^5}{1})(\frac{1}{x^4})(\frac{y^{18}}{1})=[/tex]
[tex]\frac{(2^5)(y^{18})}{(3^3)(x^4)}=[/tex]
[tex]\frac{32y^{18}}{27x^4}[/tex]
