[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}}\\\\[-0.35em]
\rule{34em}{0.25pt}\\\\
4^5\cdot 4^{-7}\div 4^{-2}\implies \cfrac{4^5\cdot 4^{-7}}{4^{-2}}\implies \cfrac{4^{5-7}}{4^{-2}}\implies \cfrac{4^{-2}}{4^{-2}}\implies 4^{-2}\cdot 4^2
\\\\\\
4^{-2+2}\implies \boxed{4^0}\implies 1 [/tex]
