Sure! Let's simplify the given expression [tex]\(\left(5 \times 10^7\right)\left(3 \times 10^{14}\right)\)[/tex] step-by-step:
1. Multiply the coefficients:
[tex]\[
5 \times 3 = 15
\][/tex]
2. Multiply the powers of 10:
[tex]\[
10^7 \times 10^{14} = 10^{7+14} = 10^{21}
\][/tex]
3. Combine the results:
[tex]\[
(5 \times 3) \times (10^7 \times 10^{14}) = 15 \times 10^{21}
\][/tex]
So, the simplified expression in scientific notation is:
[tex]\[
15 \times 10^{21}
\][/tex]
Thus, the correct answer is:
[tex]\[
\boxed{15 \times 10^{21}}
\][/tex]
