Question

We were never taught this in class, and I understand it, kind of... but i'm just confused with everything.

Answer 1

`\bf \cfrac{x^3y}{xy^5}\cdot \cfrac{x^2y^9}{x^8}\implies \cfrac{x^3x^2y^1y^9}{x^1x^8y^5} \\ \quad \\ \textit{now, using exponent rules, same base, different exponent} \\ \quad \\ \cfrac{x^(3+2)y^(1+9)}{x^(1+8)y^5}\implies \cfrac{x^5y^(10)}{x^9y^5}\\ ----------------------------\\`
`\bf \textit{now, keep in mind that} \\ \quad \\ a^{-{ n}} \implies \cfrac{1}{a^( n)}\qquad \qquad \cfrac{1}{a^( n)}\implies a^{-{ n}} \\ \quad \\ % negative exponential denominator a^{{ n}} \implies \cfrac{1}{a^(- n)} \qquad \qquad \cfrac{1}{a^(- n)}\implies \cfrac{1}{(1)/(a^( n))}\implies a^{{ n}} \\ \quad \\ thus\\ ----------------------------\\`
`\bf \cfrac{x^5y^(10)}{x^9y^5}\implies \cfrac{x^5y^(10)}{1}\cdot \cfrac{1}{x^9}\cdot \cfrac{1}{y^5}\implies x^5y^(10)\cdot x^{\boxed{-9}}\cdot y^{\boxed{-5}} \\ \quad \\ x^5x^(-9)y^(10)y^(-5)\implies x^(5-9)y^(10-5)\implies x^(-4)y^5 \\ \quad \\ \cfrac{1}{x^{\boxed{4}}}\cdot \cfrac{y^5}{1}\implies \cfrac{y^5}{x^4}`