Question

Simplify the expression ((81y^-8)/(16x^20))^-1/4

Answer 1

$\bf ~~~~~~~~~~~~\textit{negative exponents} \\\\ a^{-n} \implies \cfrac{1}{a^n} \qquad \qquad \cfrac{1}{a^n}\implies a^{-n} \qquad \qquad a^n\implies \cfrac{1}{a^{-n}} \\\\ -------------------------------$

$\bf \left( \cfrac{81y^{-8}}{16x^{20}} \right)^{-\frac{1}{4}}\implies \left( \cfrac{16x^{20}}{81y^{-8}} \right)^{\frac{1}{4}}\implies \left( \cfrac{2^4x^{20}}{3^4y^{-8}} \right)^{\frac{1}{4}} \\\\\\ \textit{and now we'll distribute the exponent}\qquad \left( \cfrac{2^{4\cdot \frac{1}{4}}x^{20\cdot \frac{1}{4}}}{3^{4\cdot \frac{1}{4}}y^{-8\cdot \frac{1}{4}}} \right) \\\\\\ \cfrac{2^1x^5}{3^1y^{-2}}\implies \cfrac{2^1x^5y^2}{3^1}\implies \cfrac{2x^5y^2}{3}$