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