Question

use the exponent function on your calculator (ee or exp) to compute the following.

(-1.6 x 10^5) (-2.4 x 10^15)
-------------------------------------
8.9 x 10^3

Answer 1

To compute the expression

\[
\frac{(-1.6 \times 10^5) \times (-2.4 \times 10^{15})}{8.9 \times 10^3}
\]

we can break it down into a few steps:

1. **Multiply the numerators**:
\[
(-1.6) \times (-2.4) = 3.84
\]
\[
10^5 \times 10^{15} = 10^{(5 + 15)} = 10^{20}
\]
Therefore,
\[
(-1.6 \times 10^5) \times (-2.4 \times 10^{15}) = 3.84 \times 10^{20}
\]

2. **Now divide by the denominator**:
\[
\frac{3.84 \times 10^{20}}{8.9 \times 10^3}
\]

First, divide the coefficients:
\[
\frac{3.84}{8.9} \approx 0.43146
\]

Now, handle the powers of ten:
\[
\frac{10^{20}}{10^3} = 10^{(20 - 3)} = 10^{17}
\]

3. **Combine the results**:
\[
0.43146 \times 10^{17}
\]

4. **Expressing in scientific notation**:
To convert \(0.43146\) to scientific notation, we write it as:
\[
4.3146 \times 10^{-1}
\]
Combining this with \(10^{17}\):
\[
4.3146 \times 10^{-1} \times 10^{17} = 4.3146 \times 10^{16}
\]

Thus, the final result is:
\[
4.3146 \times 10^{16}
\]