Question

Perform the indicated computation.
left parenthesis 3 times 10 Superscript 4 right parenthesis left parenthesis 5 times 10 squared right parenthesis
Question content area bottom
Part 1
left parenthesis 3 times 10 Superscript 4 right parenthesis left parenthesis 5 times 10 squared right parenthesisequals
  
enter your response here
​(Use scientific notation. Use the multiplication symbol in the math palette as​ needed.)

Answer 1

To compute \((3 \times 10^4)(5 \times 10^2)\), you can follow these steps:

1. **Multiply the coefficients**:
\[
3 \times 5 = 15
\]

2. **Add the exponents of 10**:
\[
10^4 \times 10^2 = 10^{4 + 2} = 10^6
\]

3. **Combine the results**:
\[
(3 \times 10^4)(5 \times 10^2) = 15 \times 10^6
\]

4. **Convert to scientific notation**:
The number \(15\) is not in proper scientific notation (it should be between 1 and 10), so we need to rewrite it:
\[
15 = 1.5 \times 10^1
\]
Thus,
\[
15 \times 10^6 = (1.5 \times 10^1) \times 10^6 = 1.5 \times 10^{1 + 6} = 1.5 \times 10^7
\]

So, the final answer is:
\[
\boxed{1.5 \times 10^7}
\]