Question

How do you simplify these problems ?

Answer 1

$\bf ~~~~~~~~~~~~\textit{negative exponents}\\\\a^{-n} \implies \cfrac{1}{a^n}\qquad \qquad\cfrac{1}{a^n}\implies a^{-n}\qquad \qquad a^n\implies \cfrac{1}{a^{-n}}\\\\[-0.35em]\rule{34em}{0.25pt}\\\\\cfrac{2x^3y^3}{4y^2}\implies \cfrac{2}{4}\cdot \cfrac{x^3y^3}{y^2}\implies \cfrac{1}{2}\cdot x^3y^3y^{-2}\implies \cfrac{1}{2}\cdot x^3y^{3-2}\implies \cfrac{x^3y}{2}\\\\~\dotfill$

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

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