Simplify the rational expression:

(5a^2*b^2*c^-3) / (2a^3)

First we can move c^-3 to the denominator as c^3 since it has a negative exponent.

(5a^2*b^2) / (2a^3*c^3)

Now we can reduce the expression. We have 'a' terms on top and bottom, so to reduce we just subtract the exponents. We have a^2 on top and a^3 on bottom, so we are left with a^1 on bottom.

(5b^2) / (2a*c^3)