To simplify this expression, we first need to apply the exponent rule for powers of a power, which states that (a^m)^n = a^(m*n).

So, for the first term: (5a^2)^3 = 5^3 (a^2)^3 = 125 a^6.

For the second term: (6b)^2 = 6^2 b^2 = 36 b^2.

Then, the expression becomes: (125 a^6) (36 * b^2) / (30a^3b)^2.

Next, we simplify the denominator: (30a^3b)^2 = 30^2 (a^3)^2 b^2 = 900 a^6 b^2.

Now, the expression becomes: (125 a^6) (36 b^2) / (900 a^6 * b^2).

We can cancel out a^6 and b^2 in the numerator and denominator: 125 * 36 / 900 = 4500 / 900 = 5.

Therefore, (5a^2)^3*(6b)^2 / (30a^3b)^2 simplifies to 5.