The concepts of dynamical scaling in the study of kinetic roughness are applied to the problem of photoresist development. Uniform, open-frame exposure and development of photoresist corresponds to the problem of quenched noise and the etching of random disordered media and is expected to fall in the Kadar-Parisi-Zhang (KPZ) universality class for the case of fast development. To verify this expectation, simulations of photoresist development in 1+1 and 2+1 dimensions were carried out with various amounts of random, uncorrelated noise added to an otherwise uniform development rate. The resulting roughness exponent and the growth exponent were found to match the KPZ values nearly exactly. The impact of the magnitude of the underlying development randomness on the values of these exponents was also determined, and an empirical expression for predicting the kinetic roughness over a wide range of conditions is presented.