Solution
brute forced this oneā¦
count = 0
for a in range(1, 10):
for b in range(1, 100):
value = a ** b
digit_count = len(str(value))
if digit_count == b:
count = count+1
print(f"{a}^{b} = {value}, digits = {digit_count}")
print(f"count = {count}")