Question

The quotient of 8.4 times 10 Superscript 9 and a number n results in 5.6 times 10 Superscript 27. What is the value of n?
1.5 times 10 Superscript negative 18
1.5 times 10 Superscript negative 3
1.5 times 10 Superscript 3

Answer 1

To solve for \( n \), we start with the equation given by the problem:

\[
\frac{8.4 \times 10^9}{n} = 5.6 \times 10^{27}
\]

To find \( n \), we can rearrange the equation to isolate \( n \):

\[
n = \frac{8.4 \times 10^9}{5.6 \times 10^{27}}
\]

Now, we calculate the fraction:

1. **Divide the coefficients**:
\[
\frac{8.4}{5.6} = 1.5
\]

2. **Subtract the exponents** (using the laws of exponents):
\[
10^9 \div 10^{27} = 10^{9-27} = 10^{-18}
\]

Now we can combine these results to find \( n \):

\[
n = 1.5 \times 10^{-18}
\]

Thus, the value of \( n \) is:

\[
\boxed{1.5 \times 10^{-18}}
\]

This matches the first option provided.