Question

Perform the indicated operations and give the answer in scientific notation.
StartFraction 8.4 times 10 Superscript negative 1 Baseline times 4.0 times 10 Superscript negative 2 Over 3 times 10 Superscript 4 Baseline times 3.2 times 10 Superscript negative 3 EndFraction
Question content area bottom
Part 1
Choose the correct answer below.
A.6.2 times 10 Superscript negative 4
6.2 times 10 Superscript negative 4
B.3.5 times 10 Superscript negative 4
3.5 times 10 Superscript negative 4
C.3.5 times 10 Superscript 14
3.5 times 10 Superscript 14
D.0.000350000
0.000350000

Answer 1

To solve the expression

\[
\frac{8.4 \times 10^{-1} \times 4.0 \times 10^{-2}}{3 \times 10^{4} \times 3.2 \times 10^{-3}},
\]

we can handle the numerical coefficients and the powers of 10 separately.

1. **Multiply the numerators**:
\[
8.4 \times 4.0 = 33.6
\]
And for the powers of 10:
\[
10^{-1} \times 10^{-2} = 10^{-3}.
\]
Thus,
\[
\text{Numerator} = 33.6 \times 10^{-3}.
\]

2. **Multiply the denominators**:
\[
3 \times 3.2 = 9.6,
\]
And for the powers of 10:
\[
10^{4} \times 10^{-3} = 10^{1}.
\]
Thus,
\[
\text{Denominator} = 9.6 \times 10^{1}.
\]

3. **Combine them into a single fraction**:
\[
\frac{33.6 \times 10^{-3}}{9.6 \times 10^{1}}.
\]

4. **Divide the coefficients**:
\[
\frac{33.6}{9.6} = 3.5.
\]

5. **Subtract the powers of ten**:
\[
10^{-3} \div 10^{1} = 10^{-3-1} = 10^{-4}.
\]

So, combining these results:
\[
3.5 \times 10^{-4}.
\]

Now we have the final result in scientific notation:
\[
3.5 \times 10^{-4}.
\]

Thus, the correct answer is **B. \(3.5 \times 10^{-4}\)**.