Question

Simplify the given expression and assume that no variable equals zero. And show your work, please.

Answer 1

$\bf \left.\qquad \qquad \right.\textit{negative exponents}\\\\ a^{-{ n}} \implies \cfrac{1}{a^{ n}} \qquad \qquad \cfrac{1}{a^{ n}}\implies a^{-{ n}} \qquad \qquad a^{{{ n}}}\implies \cfrac{1}{a^{-{{ n}}}}\\\\ -------------------------------\\\\ \left( \cfrac{32x^{18}y^{10}}{16x^9y^{20}} \right)^2\impliedby \textit{first off, let's distribute the exponent}$

$\bf \left( \cfrac{32^2x^{2\cdot 18}y^{2\cdot 10}}{16^2x^{2\cdot 9}y^{2\cdot 20}} \right)\implies \cfrac{32^2x^{36}y^{20}}{16^2x^{18}y^{40}}\implies \cfrac{32^2x^{36}x^{-18}}{16^2y^{-20}y^{40}}$

$\bf \cfrac{32^2x^{36-18}}{16^2y^{-20+40}} \implies \cfrac{32^2x^{18}}{16^2y^{20}}\implies \cfrac{32\cdot 32}{16\cdot 16}\cdot \cfrac{x^{18}}{y^{20}}\implies \cfrac{32}{16}\cdot \cfrac{32}{16}\cdot \cfrac{x^{18}}{y^{20}} \\\\\\ \cfrac{2}{1}\cdot \cfrac{2}{1}\cdot \cfrac{x^{18}}{y^{20}}\implies \cfrac{4x^{18}}{y^{20}}$