What is the digit at the 100th place of number (225)⁴⁰ ?

225⁴⁰ = (225²)²⁰ = 50625²⁰. Note 225 = 9 × 25, so 225⁴⁰ = 9⁴⁰ × 25⁴⁰ = 9⁴⁰ × 5⁸⁰. Also 225² = 50625. Looking at last three digits patterns: 225² = 50625 (last 3: 625), 225³ ends in ...625 × 225 = ...625 (since 625 × 225 = 140625, ends in 625). In fact, 225ⁿ for n ≥ 2 ends in ...0625 or similar. Computing 225² = 50625, 225³ = 11390625, 225⁴ = 2562890625. The last 3 digits stabilize at 625. So the hundreds digit (100th place) is 6.