To simplify the expression [tex]\((5 \times 10^7)(6 \times 10^4)\)[/tex] and write the answer in scientific notation, we can follow these steps:
1. Separate the Coefficients and the Powers of 10:
- The expression can be split into two parts: the coefficients and the powers of 10.
- Coefficients: [tex]\(5\)[/tex] and [tex]\(6\)[/tex]
- Powers of 10: [tex]\(10^7\)[/tex] and [tex]\(10^4\)[/tex]
2. Multiply the Coefficients:
- Multiply [tex]\(5\)[/tex] and [tex]\(6\)[/tex]:
[tex]\[
5 \times 6 = 30
\][/tex]
3. Add the Exponents in the Powers of 10:
- When you multiply powers of 10, you add the exponents:
[tex]\[
10^7 \times 10^4 = 10^{7+4} = 10^{11}
\][/tex]
4. Combine the Results:
- Combine the product of the coefficients with the new power of 10:
[tex]\[
30 \times 10^{11}
\][/tex]
5. Write the Final Answer in Scientific Notation:
- The appropriate scientific notation should have a single digit before the decimal point. Since [tex]\(30\)[/tex] can be written as [tex]\(3.0 \times 10^1\)[/tex], we can rewrite the answer as:
[tex]\[
3.0 \times 10^1 \times 10^{11} = 3.0 \times 10^{1+11} = 3.0 \times 10^{12}
\][/tex]
Thus, the simplified expression in scientific notation is:
[tex]\[
3.0 \times 10^{12}
\][/tex]
So, the correct answer is:
[tex]\[
3.0 \times 10^{12}
\][/tex]
