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)}`