The pattern in the given expression is that the exponents of "a" increase by 3 each time.

So, we can rewrite the expression as follows:

a^1.a^2.a^7....a^100 = a^(1+2+7+...+100)

Similarly,

a^1.a^2.a^3....a^2018 = a^(1+2+3+...+2018)

And,

a^2.a^5.a^8....a^2003 = a^(2+5+8+...+2003)

To find the sum of the exponents, we can use the formula for the sum of an arithmetic series:

Sum = (n/2)(first term + last term)

For the first expression, the first term is 1, the last term is 100, and the common difference is 3. So,

Sum = (100/2)(1 + 100) = 50(101) = 5050

For the second expression, the first term is 1, the last term is 2018, and the common difference is 1. So,

Sum = (2018/2)(1 + 2018) = 1009(2019) = 2035871

For the third expression, the first term is 2, the last term is 2003, and the common difference is 3. So,

Sum = (2003/2)(2 + 2003) = 1001(2005) = 2007005

Therefore, the simplified expression is:

5050.a^5050 + 2035871.a^2035871 + 2007005.a^2007005