Question

How do you simplify these problems ?

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)}\\\\[-0.35em]\rule{34em}{0.25pt}\\\\\cfrac{2x^3y^3}{4y^2}\implies \cfrac{2}{4}\cdot \cfrac{x^3y^3}{y^2}\implies \cfrac{1}{2}\cdot x^3y^3y^(-2)\implies \cfrac{1}{2}\cdot x^3y^(3-2)\implies \cfrac{x^3y}{2}\\\\~\dotfill\\\\`

`\bf \left(\cfrac{x^(-8)}{y^(11)} \right)^(-2)\implies \left(\cfrac{y^(11)}{x^(-8)} \right)^2\implies \stackrel{\textit{distributing the exponent}}{\left( \cfrac{y^(11\cdot 2)}{x^(-8\cdot 2)} \right)}\\\\\\\cfrac{y^(22)}{x^(-16)}\implies y^(22)x^(16)\\\\~\dotfill`

`\bf \cfrac{(2x^3)(x^4)^2}{8x^(11)}\implies \cfrac{(2x^3)(x^(4\cdot 2))}{8x^(11)}\implies \cfrac{2x^3x^8}{8x^(11)}\implies \cfrac{2x^(3+8)}{8x^(11)}\implies \cfrac{2x^(11)}{8x^(11)}\\\\\\\cfrac{2}{8}\cdot \cfrac{x^(11)}{x^(11)}\implies \cfrac{1}{4}\cdot 1\implies \cfrac{1}{4}`