To solve the expression [tex]\( A = \frac{96 \times 10^{-4}}{3 \times 10^{-6}} \)[/tex] and find the result in its integer form, we will follow a detailed step-by-step approach:
1. Write down the given expression:
[tex]\[
A = \frac{96 \times 10^{-4}}{3 \times 10^{-6}}
\][/tex]
2. Separate the constants and the powers of 10:
[tex]\[
A = \left(\frac{96}{3}\right) \times \left(\frac{10^{-4}}{10^{-6}}\right)
\][/tex]
3. Simplify the constants:
[tex]\[
\frac{96}{3} = 32
\][/tex]
4. Simplify the powers of 10 using the property [tex]\(\frac{10^a}{10^b} = 10^{a-b}\)[/tex]:
[tex]\[
\frac{10^{-4}}{10^{-6}} = 10^{-4 - (-6)} = 10^{-4 + 6} = 10^{2}
\][/tex]
5. Combine the simplified values:
[tex]\[
A = 32 \times 10^{2}
\][/tex]
6. Convert [tex]\(10^{2}\)[/tex] to its numerical value:
[tex]\[
10^{2} = 100
\][/tex]
7. Multiply the constants:
[tex]\[
A = 32 \times 100 = 3200
\][/tex]
Thus, the result of the expression [tex]\( A \)[/tex] in its integer form is [tex]\( \boxed{3200} \)[/tex].
Therefore, the correct answer is:
c) 3200
