To simplify the expression [tex]\(\left(9 \times 10^2\right)\left(2 \times 10^{10}\right)\)[/tex] and write the answer in scientific notation, follow these steps:
1. Identify the given terms:
- The first term is [tex]\(9 \times 10^2\)[/tex].
- The second term is [tex]\(2 \times 10^{10}\)[/tex].
2. Multiply the coefficients:
- The coefficients are 9 and 2. Multiply these together:
[tex]\[
9 \times 2 = 18
\][/tex]
3. Add the exponents of [tex]\(10\)[/tex]:
- One exponent is [tex]\(2\)[/tex] and the other is [tex]\(10\)[/tex]. Add these exponents together:
[tex]\[
2 + 10 = 12
\][/tex]
4. Combine the results:
- Now, place the product of the coefficients together with the sum of the exponents to create the scientific notation form:
[tex]\[
18 \times 10^{12}
\][/tex]
5. Adjust the format to scientific notation:
- Scientific notation requires the coefficient to be between 1 and 10. Thus, adjust [tex]\(18 \times 10^{12}\)[/tex] to fit this format:
- [tex]\(18\)[/tex] can be written as [tex]\(1.8 \times 10^1\)[/tex].
- Therefore,
[tex]\[
18 \times 10^{12} = (1.8 \times 10^1) \times 10^{12} = 1.8 \times 10^{13}
\][/tex]
The correct simplified answer in scientific notation is:
[tex]\(\boxed{1.8 \times 10^{13}}\)[/tex].
