To solve the equation (\frac{11}{33} = 2^{3x}), we need to simplify the left side first by dividing both the numerator and the denominator by 11:

[\frac{11}{33} = \frac{1}{3}]

Now, we can write the equation as:

[\frac{1}{3} = 2^{3x}]

Since 2 can be written as (2^1), we can rewrite the equation as:

[\frac{1}{3} = 2^{3x} = (2^1)^{3x} = 2^{3x} = 2^{3x} = 2^{3x}]

Now, we can see that the base on both sides are the same. Therefore, we can equate the exponents:

[3x = 1]

Dividing by 3 on both sides:

[x = \frac{1}{3}]