To find the value of M, we can first simplify the expression inside the parentheses.

The sum of a geometric series with a common ratio of 2 and a first term of 1 can be calculated using the formula:

S = a * (r^n - 1) / (r - 1)

where S is the sum of the series, a is the first term, r is the common ratio, and n is the number of terms.

In this case, a = 1, r = 2, and n = 2009. Plugging these values into the formula, we get:

S = 1 * (2^2009 - 1) / (2 - 1)
= 2^2009 - 1

Now, we can substitute this value back into the expression for M:

M = 2^2010 - (2^2009 + 2^2008 + .. +2^1 + 1)
= 2^2010 - (2^2009 - 1)
= 2^2010 - 2^2009 + 1

Since 2^2010 is equal to 2 * 2^2009, we can rewrite the expression as:

M = 2 * 2^2009 - 2^2009 + 1
= 2^2009 + 1

Therefore, the value of M is 2^2009 + 1.