Question

Simplify showing your work 9(2x^4y^2)^3/(3x^5y^3)4

Answer 1

$\bf ~\hspace{7em}\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} ~\hspace{4.5em} a^n\implies \cfrac{1}{a^{-n}} ~\hspace{4.5em} \cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m} \\\\[-0.35em] \rule{34em}{0.25pt}$

$\bf \cfrac{9(2x^4y^2)^3}{(3x^5y^3)^4}\implies \cfrac{9(2^3x^{4\cdot 3}y^{2\cdot 3})}{(3^4x^{5\cdot 4}y^{3\cdot 4})}\implies \cfrac{9(8x^{12}y^6)}{81x^{20}y^{12}}\implies \cfrac{(8x^{12}y^6)}{9x^{20}y^{12}} \\\\\\ \cfrac{8}{9}\cdot \cfrac{x^{12}y^6}{x^{20}y^{12}}\implies \cfrac{8}{9}\cdot \cfrac{1}{x^{20}x^{-12}y^{12}y^{-6}}\implies \cfrac{8}{9}\cdot \cfrac{1}{x^{20-12}y^{12-6}}\implies \cfrac{8}{9x^8y^6}$