Question

Evaluate the following expressions in scientific notation.
(2.1 x 10^4)(4x10^6)
(7.5 x 10^8)/ (1.5 x 10^3)

Answer 1

To evaluate the expressions in scientific notation, we will follow the rules for multiplying and dividing numbers in scientific notation.

### 1. Evaluating \((2.1 \times 10^4)(4 \times 10^6)\)

**Step 1: Multiply the coefficients**
\(2.1 \times 4 = 8.4\)

**Step 2: Add the exponents on the powers of 10**
\(10^4 \times 10^6 = 10^{4 + 6} = 10^{10}\)

**Step 3: Combine the results**
So, the result is:
\[
8.4 \times 10^{10}
\]

### 2. Evaluating \(\frac{(7.5 \times 10^8)}{(1.5 \times 10^3)}\)

**Step 1: Divide the coefficients**
\(\frac{7.5}{1.5} = 5.0\)

**Step 2: Subtract the exponents on the powers of 10**
\(\frac{10^8}{10^3} = 10^{8 - 3} = 10^{5}\)

**Step 3: Combine the results**
So, the result is:
\[
5.0 \times 10^{5}
\]

### Final Answers

1. \((2.1 \times 10^4)(4 \times 10^6) = 8.4 \times 10^{10}\)
2. \(\frac{(7.5 \times 10^8)}{(1.5 \times 10^3)} = 5.0 \times 10^{5}\)