Remember the following property of exponentials:
[tex]\frac{a^n}{a^m}=a^{n-m}[/tex]
The order of factors in a multiplication or division does not affect the result. Use this property to rearrange the factors, grouping those powers of 10 together:
[tex]\frac{2.5\times10^3}{4.2\times10^8}=\frac{2.5}{4.2}\times\frac{10^3}{10^8}[/tex]
Next, use the given property of exponentials to simpify the quotient that contains powers of 10:
[tex]\begin{gathered} \frac{2.5}{4.2}\times\frac{10^3}{10^8}=\frac{2.5}{4.2}\times10^{3-8} \\ =\frac{2.5}{4.2}\times10^{-5} \end{gathered}[/tex]
Calculate the quotient 2.5 / 4.2 :
[tex]\frac{2.5}{4.2}\times10^{-5}=0.5952\ldots\times10^{-5}[/tex]
Move the decimal point one place to the right, by substracting 1 from the power of 10:
[tex]0.5952\ldots\times10^{-5}=5.952\ldots\times10^{-6}[/tex]
Since the factors have 2 significant figures, round the result to 2 significant figures:
[tex]5.952\ldots\times10^{-6}\approx6.0\times10^{-6}[/tex]
Therefore, the answer is:
[tex]6.0\times10^{-6}[/tex]
