Sure, let's solve this step-by-step.
1. Write the given terms in scientific notation:
We are given:
[tex]\[
1 \times 10^4
\][/tex]
and
[tex]\[
8 \times 10^0
\][/tex]
2. Multiply the numerical coefficients:
Take the coefficients [tex]\(1\)[/tex] and [tex]\(8\)[/tex] and multiply them together:
[tex]\[
1 \times 8 = 8
\][/tex]
3. Add the exponents of the powers of 10:
Now, the exponents [tex]\(4\)[/tex] (from [tex]\(10^4\)[/tex]) and [tex]\(0\)[/tex] (from [tex]\(10^0\)[/tex]) need to be added together:
[tex]\[
10^4 \times 10^0 = 10^{4+0} = 10^4
\][/tex]
4. Combine the results:
Multiply the result from step 2 (the numerical coefficient) with the result from step 3 (the power of 10):
[tex]\[
8 \times 10^4
\][/tex]
Therefore, the product in scientific notation is:
[tex]\[
8.00 \times 10^4
\][/tex]
