To divide these two terms, we can rationalize the denominators.
First, we rationalize the denominator of the first term, which is √13.
Multiplying the numerator and denominator of the first term by √13, we get:
36√39 * √13 / (9√13 * √13)
Simplifying the denominator, we have:
36√39 * √13 / (9 * 13)
Multiplying the denominators, we get:
36√39 * √13 / 117
Again, we rationalize the denominator, which is 117.
Multiplying the numerator and denominator by √117, we have:
(36√39 * √13 * √117) / (117 * √117)
Simplifying the numerator and denominator:
36 * √(39 * 13 * 117) / (117 * √(117 * 117))
The square root of 39 * 13 * 117 is √{3^2 * 13 * (3*13) * 117} = 3 * 13 * √(3 * 13) = 39√(3 * 13).
The square root of 117 * 117 = √{3^2 * 13^2} = 3 * 13 = 39.
Substituting these values, we have:
(36 * 39√(3 * 13)) / (117 * 39)
The 39 in the numerator and denominator can be canceled out:
36√(3 * 13) / 117
The √(3 * 13) is √39.
Therefore, the final answer is:
36√39 / 117√39 = 36 / 117 = 4/13.
So, the exact answer is 4/13.