express the prime factorization 2 remainder 3 . 5 remainder 2 . 11 as a whole number

To express the prime factorization \(2 \, \text{remainder} \, 3 \cdot 5 \, \text{remainder} \, 2 \cdot 11\) as a whole number, we first need to interpret what "remainder" means in this context. It appears that each prime factor is followed by a "remainder" that indicates the exponent in its prime factorization.

Here, the expression seems to mean:

- \(2\) with a remainder of \(3\), which can be interpreted as \(2^3\)
- \(5\) with a remainder of \(2\), which can be interpreted as \(5^2\)
- and \(11\) with no remainder specified, which is \(11^1\) or simply \(11\)

Thus, we can rewrite the expression as:

\[
2^3 \cdot 5^2 \cdot 11^1
\]

Now, we can calculate the whole number:

1. **Calculate \(2^3\)**:
\[
2^3 = 8
\]

2. **Calculate \(5^2\)**:
\[
5^2 = 25
\]

3. **Combine them**:
\[
8 \cdot 25 = 200
\]

4. **Now multiply by \(11\)**:
\[
200 \cdot 11 = 2200
\]

Thus, the whole number is \(2200\).