Simplify (1/4 ad^3) ^2

That "ad^3" bothers me; I'm not sure what you mean here.

I'm going to assume that you have (1/4*a*d^3) ^2.

If that's the case, then you have (1/4) ^2 * a^2 * d^6 = (1/16) * a^2*d^6.

If this is not what you were hoping for, double check to ensure that you have copied down this problem exactly as it was presented.