To simplify the expression [tex]\((8 \times 10^{-5})(7 \times 10^{-3})\)[/tex] and write the answer in scientific notation, follow these steps:
1. Multiply the decimal numbers (bases): Multiply [tex]\(8\)[/tex] by [tex]\(7\)[/tex].
[tex]\[
8 \times 7 = 56
\][/tex]
2. Add the exponents: Add the exponents of [tex]\(10\)[/tex]. In this case, [tex]\(-5\)[/tex] and [tex]\(-3\)[/tex].
[tex]\[
-5 + -3 = -8
\][/tex]
3. Write the product in scientific notation: Combine the result from step 1 and step 2. Thus, the expression in scientific notation is:
[tex]\[
56 \times 10^{-8}
\][/tex]
4. Adjust the scientific notation: To express the number in proper scientific notation ([tex]\(a \times 10^b\)[/tex] where [tex]\(1 \leq a < 10\)[/tex]), convert [tex]\(56\)[/tex] into [tex]\(5.6 \times 10^1\)[/tex]. Then combine this with [tex]\(10^{-8}\)[/tex]:
[tex]\[
56 \times 10^{-8} = (5.6 \times 10^1) \times 10^{-8} = 5.6 \times 10^{-7}
\][/tex]
Thus, the simplified expression in scientific notation is:
[tex]\[
5.6 \times 10^{-7}
\][/tex]
The correct answer is:
[tex]\[
\boxed{A. \, 5.6 \times 10^{-7}}
\][/tex]
