We have to find the value of k in the expression:
[tex]10^{-3}\cdot10\cdot10^k=10^{-3}[/tex]
We can apply the rules for exponents and write:
[tex]\begin{gathered} 10^{-3}\cdot10^1\cdot10^k=10^{-3} \\ 10^{-3+1+k}=10^{-3} \\ -3+1+k=-3 \\ 1+k=0 \\ k=-1 \end{gathered}[/tex]
Answer: k = -1 [second option]
