To simplify the expression √3 - 1/3√27 + 2√507, we can simplify each term separately.

First, let's simplify √3. Since 3 is not a perfect square, we cannot simplify it further. Therefore, √3 remains as √3.

Next, let's simplify 1/3√27. We can simplify the square root of 27 by finding the largest perfect square that divides evenly into 27, which is 9. So, √27 = √(9 * 3) = √9 * √3 = 3√3. Therefore, 1/3√27 = 1/3 * 3√3 = √3.

Finally, let's simplify 2√507. We can simplify the square root of 507 by finding the largest perfect square that divides evenly into 507. The largest perfect square that divides evenly into 507 is 169 (13^2). So, √507 = √(169 * 3) = √169 * √3 = 13√3. Therefore, 2√507 = 2 * 13√3 = 26√3.

Now, we can substitute these simplified terms back into the original expression:

√3 - 1/3√27 + 2√507 = √3 - √3 + 26√3

Since the square root terms have the same radical (√3), we can combine them:

√3 - √3 + 26√3 = 26√3

Therefore, the simplified expression is 26√3.