[tex]\bf ~\hspace{7em}\textit{negative exponents}
\\\\
a^{-n} \implies \cfrac{1}{a^n}
~\hspace{4.5em}
a^n\implies \cfrac{1}{a^{-n}}
~\hspace{4.5em}
\cfrac{a^n}{a^m}\implies a^na^{-m}\implies a^{n-m}
\\\\[-0.35em]
\rule{34em}{0.25pt}[/tex]
[tex]\bf \left( -4\cdot \cfrac{1}{2} \right)^2\left( \cfrac{25}{4} \right)^2\implies \stackrel{\mathbb{PEMDAS}}{\left( -2 \right)^2\left( \cfrac{25^2}{4^2} \right)}\implies (-2)(-2)\cdot \cfrac{625}{(2^2)^2}\implies 2^2\cdot \cfrac{625}{2^{2\cdot 2}}
\\\\\\
\cfrac{2^2\cdot 625}{2^4}\implies \cfrac{625}{2^{-2}\cdot 2^4}\implies \cfrac{625}{2^{-2+4}}\implies \cfrac{625}{2^2}\implies \cfrac{625}{4}\implies 156\frac{1}{4}[/tex]
