Alright, let's solve the expression step-by-step.
The problem we are given is:
[tex]\[
\frac{\left(3.0 \times 10^4\right)}{\left(4.0 \times 10^8\right)}
\][/tex]
First, decompose the expression into two parts: the numerical coefficients and the powers of 10.
1. The numerical coefficient part is:
[tex]\[
\frac{3.0}{4.0}
\][/tex]
2. The powers of 10 part is:
[tex]\[
\frac{10^4}{10^8}
\][/tex]
You will want to handle each part separately.
Step 1: Divide the numerical coefficients:
[tex]\[
\frac{3.0}{4.0}
\][/tex]
This division gives:
[tex]\[
0.75
\][/tex]
Step 2: Divide the powers of 10:
[tex]\[
\frac{10^4}{10^8}
\][/tex]
Using the exponent rule for division, [tex]\(a^{m} / a^{n} = a^{m-n}\)[/tex]:
[tex]\[
10^{4-8} = 10^{-4}
\][/tex]
Step 3: Combine the results from steps 1 and 2:
Multiplying the results obtained from the numerical part and the power of 10 part:
[tex]\[
0.75 \times 10^{-4}
\][/tex]
This is the final value when the original expression is simplified.
However, for the specific problem question asking for the division of the coefficients only:
[tex]\[
3.0 \div 4.0 = 0.75
\][/tex]
So, the correct answer to the question "What is the result when you divide the coefficients?" is:
[tex]\[
0.75
\][/tex]
