To simplify the expression [tex]\( 8 \left( 8.8 \times 10^{12} \right) \)[/tex] and write the answer in scientific notation, let's go through the steps carefully:
1. Identify the components of the expression:
- The expression consists of a multiplier (8) and a number in scientific notation ([tex]\(8.8 \times 10^{12}\)[/tex]).
2. Distribute the multiplier:
- Multiply the coefficient (8.8) by the multiplier (8).
[tex]\[
8.8 \times 8 = 70.4
\][/tex]
3. Keep the exponent the same:
- The exponent in the scientific notation ([tex]\(10^{12}\)[/tex]) remains unchanged during the multiplication.
4. Combine the results:
- The new coefficient is 70.4, and the exponent is still 12. Hence, the expression becomes [tex]\( 70.4 \times 10^{12} \)[/tex].
Given this detailed breakdown, the simplified expression is:
[tex]\[
70.4 \times 10^{12}
\][/tex]
So, the correct answer, written in scientific notation, is:
[tex]\[
70.4 \times 10^{12}
\][/tex]
Among the given options:
- [tex]\(1.68 \times 10^{13}\)[/tex]
- [tex]\(70.4 \times 10^{12}\)[/tex] ([tex]\(\text{Correct Answer}\)[/tex])
- [tex]\(7.04 \times 10^{13}\)[/tex]
- [tex]\(70.4 \times 10^{24}\)[/tex]
The correct choice is:
[tex]\[
70.4 \times 10^{12}
\][/tex]
