Finding the rightmost non-zero digit of an exponential number

Break the base down to isolate the trailing zeros from the significant trailing digits: 30^30 = (3 × 10)^30 = 3^30 × 10^30.

The term 10^30 generates exactly 30 trailing zeros. The rightmost digit preceding these zeros is entirely determined by the units digit of ⟨MATH⟩3^30⟨/MATH⟩.

Find the unit digit cycle for base 3. The powers of 3 cycle through a length of 4: 3^1 = 3, 3² = 9, 3³ = 7, 3^4 = 1. Divide the exponent 30 by the cycle length 4: 30 \div 4 = 7 with a remainder of 2. A remainder of 2 points to the second position in our unit pattern, which is 9.

Answer: (d).