Question

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

(6.02 x 10^23) (-5.11 x 10^-27)
-------------------------------------
-8.23 x 10^5

Answer 1

To compute the expression:

\[
\frac{(6.02 \times 10^{23}) \times (-5.11 \times 10^{-27})}{-8.23 \times 10^{5}}
\]

Let's break it down step by step.

1. **Calculate the numerator:**

\[
6.02 \times 10^{23} \times (-5.11 \times 10^{-27}) = -30.7492 \times 10^{(23 + (-27))} = -30.7492 \times 10^{-4}
\]

To express it in a proper scientific notation, we would write:

\[
-30.7492 \times 10^{-4} = -3.07492 \times 10^{-3} \quad (\text{moving the decimal point to the left})
\]

2. **Now, divide the result by the denominator:**

\[
-3.07492 \times 10^{-3} \div (-8.23 \times 10^{5})
\]

First, let's divide the coefficients:

\[
\frac{-3.07492}{-8.23} = 0.3733 \quad (\text{approximately})
\]

Now, handle the powers of ten:

\[
10^{-3} \div 10^{5} = 10^{-3 - 5} = 10^{-8}
\]

3. **Combine the results:**

\[
0.3733 \times 10^{-8}
\]

In scientific notation, it is better expressed as:

\[
3.733 \times 10^{-9}
\]

Thus, the final result is:

\[
\boxed{3.733 \times 10^{-9}}
\]