Hopefully I am reading this correctly, but I would start by factoring the numbers and then separating them.

32 = 2^5

27 = 3^3

18 = 2 * 3^2

sqrt(3) = 3^1/2

So, the original form can be rewritten as:

(32/2) * 1/(3^3*3^2*3^(1/2))

which can be reduced to

16/(3^(11/2)) or 16/(3^5.5)

The exponent of 5.5 is found by adding 3 + 2 + 0.5 since multiplying numbers with the same base, which in this case is 3, and different exponents requires that they be added.

Now, our task is to express it in the form of 2^a * 3^b.

16 = 2^4

So, the fraction looks like:

(2^4)/(3^5.5)

Since 3^5.5 is in the denominator, the exponent becomes negative, and the final result looks like:

2^4 * 3^-5.5 or 2^4 * 3^(-11/2)

I hope this is helpful.