[tex]\bf 10^{k-3}=m\implies 10^k\cdot 10^{-3}=m\\
----------------------------\\
\textit{now, bear in mind that}\\
a^{-{ n}} \implies \cfrac{1}{a^{ n}}\qquad \qquad
\cfrac{1}{a^{ n}}\implies a^{-{ n}}
\\ \quad \\
----------------------------\\
thus
\\ \quad \\
10^k\cdot 10^{-3}=m\implies 10^k\cdot \cfrac{1}{10^{+3}}=m\implies 10^k\cdot \cfrac{1}{10^{3}}=m
\\ \quad \\
10^k\cdot \cfrac{1}{1000}=m\implies 10^k=1000m[/tex]
