[tex]\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}}
\\\\
-------------------------------[/tex]
[tex]\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}[/tex]
