A 3 digit palindrome is a 3 digit number (not starting with zero) which reads the same backwards as forwards For example, 242. The sum of all even 3 digit palindromes is `2^(n_(1))*3^(n_(2))*5^(n_(3))*7^(n_(4))*11^(n_(5))*` value of `n_(1)+n_(2)+n_(3)+n_(4)+n_(5)` is

Explanation

To solve the problem of finding the sum of all even 3-digit palindromes and expressing it in the form \(2^{n_1} \cdot 3^{n_2} \cdot 5^{n_3} \cdot 7^{n_4} \cdot 11^{n_5}\), we will follow these steps:

### Step 1: Identify the form of 3-digit palindromes
A 3-digit palindrome can be represented as \(aba\), where \(a\) is the first and last digit, and \(b\) is the middle digit. Since we are looking for even palindromes, \(a\) must be an even digit.

### Step 2: Determine the possible values for \(a\) and \(b\)
- The digit \(a\) can take the values \(2, 4, 6, 8\) (even digits, since the number must be even).
- The digit \(b\) can take any digit from \(0\) to \(9\).
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