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: 
Given the equation:

$10^{n}=9.3\times10^{-6}$

Take $\log\_{10}$ on each side:

$n=\log\_{10}(9.3\times10^{-6})$

Simplify the right-hand side:

$n=\log\_{10}(9.3)+\log\_{10}(10^{-6})$

Simplify the right-hand side again:

$n=\log\_{10}(9.3)+(-6)$

Solve the right-hand side in a calculator:

$n\approx-5.03$
If it is in form of $a\times 10^b$, then it is $10^x$ where $x=\log\_{10}(a)+b$.