Solution

brute forced this one…

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}")

References

Project Euler - 63