`10xx20xx30xx40xx------xx1000`

Answer

To solve the expression \(10 \times 20 \times 30 \times 40 \times \ldots \times 1000\), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Pattern**:
The sequence can be rewritten as \(10 \times 20 \times 30 \times 40 \times \ldots \times 1000\). Each term in this sequence can be expressed as \(10n\) where \(n\) is an integer from 1 to 100.

2. **Factor Out the Common Term**:
We can factor out \(10\) from each term:
\[ 10 \times 20 \times 30 \times 40 \times \ldots \times 1000 = 10^1 \times 10^2 \times 10^3 \times \ldots \times 10^{100} \]
This can be simplified to:
\[ 10^{1+2+3+\ldots+100} \]

3. **Calculate the Exponent**:
The sum \(1 + 2 + 3 + \ldots + 100\) can be calculated using the formula for the sum of the first \(n\) natural numbers:
\[ \text{Sum} = \frac{n(n + 1)}{2} \]
For \(n = 100\):
\[ \text{Sum} = \frac{100 \times 101}{2} = 5050 \]

4. **Write the Expression**:
Now we can rewrite the expression:
\[ 10^{5050} \]

5. **Factorial Representation**:
Additionally, we can express the product of integers from 1 to 100 as \(100!\):
\[ 10^{100} \times (1 \times 2 \times 3 \times \ldots \times 100) = 10^{100} \times 100! \]

6. **Final Answer**:
Therefore, the condensed form of the expression \(10 \times 20 \times 30 \times 40 \times \ldots \times 1000\) is:
\[ 10^{100} \times 100! \]