Sure! Let's solve the given expression step by step:
We need to evaluate the fraction:
[tex]\[
\frac{\left(0.000027 \times 10^{16}\right)\left(0.324 \times 10^{-8}\right)}{\left(0.0081 \times 10^{-5}\right)\left(30000 \times 10^{-10}\right)}
\][/tex]
To do this, we will break it down into smaller parts, handling both the numerators and the denominators separately before combining them into the final fraction.
Step 1: Evaluate the individual components
Numerator Components:
1. [tex]\(0.000027 \times 10^{16}\)[/tex]
2. [tex]\(0.324 \times 10^{-8}\)[/tex]
Denominator Components:
1. [tex]\(0.0081 \times 10^{-5}\)[/tex]
2. [tex]\(30000 \times 10^{-10}\)[/tex]
Step 2: Calculate each component
For the numerators:
1. [tex]\(0.000027 \times 10^{16} = 270,000,000,000\)[/tex] (or [tex]\(2.7 \times 10^{11}\)[/tex])
2. [tex]\(0.324 \times 10^{-8} = 3.24 \times 10^{-9}\)[/tex]
For the denominators:
1. [tex]\(0.0081 \times 10^{-5} = 8.1 \times 10^{-8}\)[/tex]
2. [tex]\(30000 \times 10^{-10} = 3.0 \times 10^{-6}\)[/tex]
Step 3: Multiply the components
Numerator:
[tex]\[ (2.7 \times 10^{11}) \times (3.24 \times 10^{-9}) = 874.8 \][/tex]
Denominator:
[tex]\[ (8.1 \times 10^{-8}) \times (3.0 \times 10^{-6}) = 2.43 \times 10^{-13} \][/tex]
Step 4: Divide the multiplied components
[tex]\[ \frac{874.8}{2.43 \times 10^{-13}} = 3600000000000000 \][/tex]
So, the final result of the expression is:
[tex]\[
3.6 \times 10^{15}
\][/tex]
or
[tex]\[
3,600,000,000,000,000
\][/tex]
