Sure, let's break down the solution for the given fraction step-by-step:
We need to evaluate the fraction:
[tex]\[
\frac{24}{(3, 13, 3, 5, 4, 5, 24)}
\][/tex]
### Step 1: Understand the Structure
The given format seems to suggest that we have a numerator [tex]\(24\)[/tex] and multiple values in the denominator. It implies we need to multiply all these values together to form a single denominator.
### Step 2: Multiply the Denominator Values
Let's multiply the values in the denominator together:
[tex]\[
3 \times 13 \times 3 \times 5 \times 4 \times 5 \times 24
\][/tex]
First, we can pair and multiply:
[tex]\[
(3 \times 13) = 39
\][/tex]
[tex]\[
(39 \times 3) = 117
\][/tex]
[tex]\[
(117 \times 5) = 585
\][/tex]
[tex]\[
(585 \times 4) = 2340
\][/tex]
[tex]\[
(2340 \times 5) = 11700
\][/tex]
[tex]\[
(11700 \times 24) = 280800
\][/tex]
So, the product of the denominators is:
[tex]\[
\text{Denominator} = 280800
\][/tex]
### Step 3: Divide the Numerator by the Denominator
Now, we need to divide the numerator by the product of the denominators:
[tex]\[
\frac{24}{280800}
\][/tex]
### Step 4: Simplify the Fraction
Perform the division:
[tex]\[
24 \div 280800 \approx 0.00008547008547008547
\][/tex]
### Intermediate and Final Results
Thus, we have:
[tex]\[
\text{Product of denominators} = 280800
\][/tex]
[tex]\[
\text{Final result} = 0.00008547008547008547
\][/tex]
Written in scientific notation, this is approximately:
[tex]\[
8.547008547008547 \times 10^{-5}
\][/tex]
Thus, the final fraction result is [tex]\(\boxed{0.00008547008547008547}\)[/tex] and the product of the denominators is [tex]\(280800\)[/tex].
