In this lesson, we developed a rule for multiplying powers of 10: Multiplying powers of 10 corresponds to adding the exponents together. 

To see this, multiply $10^2$ and $10^3$. We know that $10^2$ has two factors that are 10 and that $10^3$ has three factors that are 10. That means that $10^2\boldcdot10^3$ has 5 factors that are 10. 

This will work for other powers of 10, too. For example, $10^{14} \boldcdot 10^{47} = 10^{(14+47)}=10^{61}$.