Question

What is the product of 2, point, 2, times, 10, to the power 62.2×10
6
and 5, point, 7, times, 10, to the power 45.7×10
4
expressed in scientific notation?

Answer 1

To find the product of \(2.2 \times 10^{62.2 \times 10^6}\) and \(5.7 \times 10^{45.7 \times 10^4}\), we first need to evaluate the powers of ten.

1. **Calculate the powers of ten**:
- \(62.2 \times 10^6 = 62200000\)
- \(45.7 \times 10^4 = 457000\)

2. **Now we express the two numbers**:
- First number: \(2.2 \times 10^{62200000}\)
- Second number: \(5.7 \times 10^{457000}\)

3. **Now multiply the two expressions**:
\[
(2.2 \times 10^{62200000}) \times (5.7 \times 10^{457000}) = (2.2 \times 5.7) \times (10^{62200000 + 457000})
\]

4. **Calculate \(2.2 \times 5.7\)**:
\[
2.2 \times 5.7 = 12.54
\]

5. **Now add the exponents of 10**:
\[
62200000 + 457000 = 62657000
\]

6. **Combine the results**:
\[
12.54 \times 10^{62657000}
\]

7. **Convert to scientific notation**:
Since \(12.54\) is greater than \(10\), we express it as:
\[
1.254 \times 10^1
\]
Thus,
\[
12.54 \times 10^{62657000} = 1.254 \times 10^1 \times 10^{62657000} = 1.254 \times 10^{62657001}
\]

8. **Final result**:
The final product expressed in scientific notation is:
\[
\boxed{1.254 \times 10^{62657001}}
\]