Answered

Write the expression as a number in scientific notation.

[tex]\[
\frac{(8 \times 10^2)(3.2 \times 10^5)}{4 \times 10^3}
\][/tex]

A. [tex]\(7.2 \times 10^7\)[/tex]

B. [tex]\(7.2 \times 10^4\)[/tex]

C. [tex]\(6.4 \times 10^7\)[/tex]

D. [tex]\(6.4 \times 10^4\)[/tex]



Answer :

To solve the given expression and write the result in scientific notation, let's start by breaking down the calculations step by step.

### Step 1: Understanding the Expression

The expression we need to solve is given as:
[tex]\[ \frac{\left(8 \times 10^2\right)\left(3.2 \times 10^5\right)}{4 \times 10^3} \][/tex]

### Step 2: Multiplying the Numerator

First, let's multiply the terms in the numerator:
[tex]\[ (8 \times 10^2) \times (3.2 \times 10^5) \][/tex]

Separate the numerical coefficients and powers of 10:
[tex]\[ 8 \times 3.2 = 25.6 \][/tex]
[tex]\[ 10^2 \times 10^5 = 10^{2+5} = 10^7 \][/tex]

Thus, the product of the numerator is:
[tex]\[ 25.6 \times 10^7 \][/tex]

### Step 3: Dividing by the Denominator

Now, we divide the result from the numerator by the denominator:
[tex]\[ \frac{25.6 \times 10^7}{4 \times 10^3} \][/tex]

Separate the numerical coefficients and powers of 10 for division:
[tex]\[ \frac{25.6}{4} = 6.4 \][/tex]
[tex]\[ \frac{10^7}{10^3} = 10^{7-3} = 10^4 \][/tex]

Thus, the result of the division is:
[tex]\[ 6.4 \times 10^4 \][/tex]

### Step 4: Conclusion

The given mathematical expression simplifies to:
[tex]\[ 6.4 \times 10^4 \][/tex]

So, the correct answer is:
[tex]\[ \boxed{6.4 \times 10^4} \][/tex]