\(\bf 4^{-5}?\qquad \textit{well, bear in mind that}\\
----------------------------\\
a^{-{ n}} \implies \cfrac{1}{a^{ n}}\qquad \qquad
\cfrac{1}{a^{ n}}\implies a^{-{ n}}
\\ \quad \\
% negative exponential denominator
a^{{ n}} \implies \cfrac{1}{a^{- n}}
\qquad \qquad
\cfrac{1}{a^{- n}}\implies \cfrac{1}{\frac{1}{a^{ n}}}\implies a^{{ n}}\\
----------------------------\\
thus\implies 4^{-5}\implies \cfrac{1}{4^{+5}}\implies \cfrac{1}{4^5}\implies \cfrac{1}{1024}\)