Question

What is the value of k in the product of powers below?110 10.10 - 10-³==10³0 -3AO-1O 0O 1

Answer 1

We have to find the value of k in the expression:

$10^{-3}\cdot10\cdot10^k=10^{-3}$

We can apply the rules for exponents and write:

$\begin{gathered} 10^{-3}\cdot10^1\cdot10^k=10^{-3} \\ 10^{-3+1+k}=10^{-3} \\ -3+1+k=-3 \\ 1+k=0 \\ k=-1 \end{gathered}$

Answer: k = -1 [second option]