Question

Simplify. Final answers must be written in correct scientific notation. You must show ALL work to earn full credit.

(8 x 10^-2) ( 9x10^8)

Answer 1

To simplify the expression \((8 \times 10^{-2}) (9 \times 10^{8})\), we can use the properties of multiplication and exponential notation.

Here are the steps:

1. **Multiply the coefficients**:
\[
8 \times 9 = 72
\]

2. **Add the exponents of the powers of ten**:
\[
10^{-2} \times 10^{8} = 10^{-2 + 8} = 10^{6}
\]

3. **Combine the results**:
\[
72 \times 10^{6}
\]

4. **Convert to scientific notation**:
In scientific notation, we want the coefficient to be between 1 and 10. To convert \(72\) to scientific notation, we write it as \(7.2 \times 10^{1}\):

Thus:
\[
72 \times 10^{6} = (7.2 \times 10^{1}) \times 10^{6}
\]

5. **Combine the powers of ten again**:
\[
(7.2 \times 10^{1}) \times 10^{6} = 7.2 \times 10^{1 + 6} = 7.2 \times 10^{7}
\]

So, the final answer in correct scientific notation is:
\[
\boxed{7.2 \times 10^{7}}
\]