Question

Perform the indicated operation. Write the answer in scientific notation.
left parenthesis 6.92 times 10 Superscript 5 Baseline right parenthesis left parenthesis 5.76 x 10 squared right parenthesis
Question content area bottom
Part 1
A.4 times 10 Superscript 10
4 times 10 Superscript 10
B.3.99 times 10 Superscript 10
3.99 times 10 Superscript 10
C.3.99 times 10 Superscript 8
3.99 times 10 Superscript 8
D.4 times 10 Superscript 8
4 times 10 Superscript 8

Answer 1

To perform the operation \((6.92 \times 10^5) (5.76 \times 10^2)\), we can use the following steps:

1. Multiply the coefficients (the numbers in front):
\[
6.92 \times 5.76
\]

2. Multiply the powers of ten:
\[
10^5 \times 10^2 = 10^{5+2} = 10^7
\]

Now, let's calculate the product of the coefficients:

\[
6.92 \times 5.76 = 39.9072
\]

Now, we combine these results:
\[
39.9072 \times 10^7
\]

Next, we need to express this in proper scientific notation. The coefficient must be between 1 and 10. To convert \(39.9072\) to scientific notation, we rewrite it as \(3.99072 \times 10^1\).

So we have:
\[
39.9072 \times 10^7 = 3.99072 \times 10^1 \times 10^7 = 3.99072 \times 10^{1+7} = 3.99072 \times 10^8
\]

Rounding \(3.99072\) to \(3.99\) for easier notation gives:
\[
3.99 \times 10^8
\]

Thus, the final answer in scientific notation is:
\[
\boxed{3.99 \times 10^8}
\]

This corresponds to option C: \(3.99 \times 10^8\).