Question

`\frac{ {3x}^(2) }{xy} * \frac{ {4xy}^(2) }{ (1)/(y) }`

Answer 1

`\bf ~~~~~~~~~~~~\textit{negative exponents} \\\\ a^(-n) \implies \cfrac{1}{a^n} \qquad \qquad \cfrac{1}{a^n}\implies a^(-n) \qquad \qquad a^n\implies \cfrac{1}{a^(-n)} \\\\ -------------------------------\\\\ \cfrac{3x^2}{xy}\cdot \cfrac{4xy^2}{(1)/(y)}\implies \cfrac{3x^2}{xy}\cdot \cfrac{4xy^2}{y^(-1)}\implies \cfrac{3x^2x^1y^2}{xy^1y^(-1)}\implies \cfrac{3x^(2+1)y^2}{xy^(1-1)} \\\\\\ \cfrac{3x^3y^2}{xy^0}\implies \cfrac{3x^3y^2}{x^1}\implies 3x^3y^2x^(-1)\implies 3x^(3-1)y^2\implies 3x^2y^2`