To compare the given numbers, we can express them with a common exponent or a common base. For instance, 4^18 can be written as (2^2)^18 = 2^36, and 8^12 can be written as (2^3)^12 = 2^36. Thus, 4^18 and 8^12 are equal. Comparing 2^40, 3^21, and 2^36, it is evident that 2^36 is smaller than 2^40. To compare 2^36 and 3^21, we can raise both to a power that makes them easier to compare, or consider their approximate values. However, a systematic approach involves finding a common exponent. By rewriting 3^21 as (3^3)^7 = 27^7 and 2^40 as (2^4)^10 = 16^10, or by making exponents similar, we observe that 3^21 is the smallest.