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}`