Question

Can someone help me with this quick? Thank you!

Answer 1

remember that (ab)/(cd)=(a/c)(b/c)

also remember that $(a^b)^c=a^{bc}=(a^c)^b$

also, $\frac{a^b}{a^c}=a^{b-c}$ and $a^{-b}=\frac{1}{a^b}$ and $(ab)^c=(a^c)(b^c)$

group the like bits together

$\frac{3(2x^4y^6)^5}{(3x^6y^3)^4}=$

$\frac{3(2^5)((x^4)^5)((y^6)^5)}{(3^4)((x^6)^4)((y^3)^4)}=$

$\frac{(3^1)(2^5)(x^{20})(y^{30})}{(3^4)(x^{24})(y^{12})}=$

$(\frac{3^1}{3^4})(\frac{2^5}{1})(\frac{x^{20}}{x^{24}})(\frac{y^{30}}{y^{12}})=$

$(3^{1-4})(2^5)(x^{20-24})(y^{30-12})=$

$(3^{-3})(2^5)(x^{-4})(y^{18})=$

$(\frac{1}{3^3})(\frac{2^5}{1})(\frac{1}{x^4})(\frac{y^{18}}{1})=$

$\frac{(2^5)(y^{18})}{(3^3)(x^4)}=$

$\frac{32y^{18}}{27x^4}$