To solve the problem of dividing:
[tex]\[ \frac{\left(3.0 \times 10^4\right)}{\left(4.0 \times 10^8\right)} \][/tex]
we can break it down step-by-step.
### Step 1: Divide the Coefficients
First, we need to divide the numerical coefficients (3.0 and 4.0):
[tex]\[ \frac{3.0}{4.0} = 0.75 \][/tex]
### Step 2: Divide the Powers of Ten
Next, we divide the powers of ten:
[tex]\[ \frac{10^4}{10^8} = 10^{4-8} = 10^{-4} \][/tex]
### Step 3: Combine the Results
Now, we combine the coefficient result with the power of ten result:
[tex]\[ 0.75 \times 10^{-4} \][/tex]
### Converting to Scientific Notation
To express [tex]\( 0.75 \times 10^{-4} \)[/tex] in a common scientific notation, we must convert 0.75 into a value between 1 and 10. This can be done as:
[tex]\[ 0.75 = 7.5 \times 10^{-1} \][/tex]
So,
[tex]\[ 0.75 \times 10^{-4} = (7.5 \times 10^{-1}) \times 10^{-4} = 7.5 \times 10^{-5} \][/tex]
### Final Result
Therefore, the final result of the division is:
[tex]\[ 7.5 \times 10^{-5} \][/tex]
### Answer to the Question
The result when you divide the powers of ten:
[tex]\[ 10^4 \div 10^8 = 10^{4-8} = 10^{-4} \][/tex]
Among the given options ( [tex]$-4$[/tex], 12, 32, 0.5 ), the correct exponent value for this division is:
[tex]\[ \boxed{-4} \][/tex]
