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Multiplication and division with powers of ten

Problem

Quinn tried to evaluate an expression step by step.
(3104)0.002=(3104)(2103)Step 1=(32)(104103)Step 2=6101Step 3\qquad\begin{aligned} &(3 \cdot 10^4) \cdot 0.002 \\\\ \\ =&(3 \cdot 10^4) \cdot (2\cdot10^{-3})&\green{\text{Step } 1}\\\\ \\ =&(3\cdot2)\cdot(10^4\cdot10^{-3})&\blue{\text{Step } 2}\\\\ \\ =&6 \cdot10^1&\purple{\text{Step } 3} \\\\ \end{aligned}
Find Quinn's mistake.
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