Question: How to convert a number to $10^n$?

For example, $9.3\times10^{-6}=10^{-5.03}$.

How do you do this conversion to calculate the exponent of $10$?

How does one calculate the $-5.03$ exponent?

Answer: 
What you are basically saying is that you have a number $a$ and you want to find some number $x$ such that

$$10^x = a.$$

You can solve the equation above by applying the $\log\_{10}$ function on both sides to get

$$\log\_{10}(10^x) = \log\_{10}(a).$$

Now, remember what the $\log$ function is, and you are done.
If it is in form of $a\times 10^b$, then it is $10^x$ where $x=\log\_{10}(a)+b$.