Certainly! Let's perform the multiplication and express the answer in proper scientific notation.
1. Identify the given values:
[tex]\[
a = 2.60 \times 10^{-5} \][/tex]
[tex]\[
b = 2.10 \times 10^{-5}
\][/tex]
2. Multiply the significant figures:
[tex]\[
(2.60) \times (2.10) = 5.46
\][/tex]
3. Multiply the powers of 10:
Using the property of exponents [tex]\(10^a \times 10^b = 10^{a+b}\)[/tex]:
[tex]\[
10^{-5} \times 10^{-5} = 10^{-10}
\][/tex]
4. Combine the results to get the product:
[tex]\[
(2.60 \times 10^{-5}) \times (2.10 \times 10^{-5}) = 5.46 \times 10^{-10}
\][/tex]
5. Express in scientific notation:
The result of the multiplication is already in scientific notation.
[tex]\[
5.46 \times 10^{-10}
\][/tex]
Therefore, the product of [tex]\(2.60 \times 10^{-5} \times 2.10 \times 10^{-5}\)[/tex] is:
[tex]\[
5.46 \times 10^{-10}
\][/tex]
