Your algorithm needs an iteration your implementation doesn't provide. Try
def raise_to_power_1(base1, power1):
i = 0
result1 = 1
while True:
if i < power1:
result1 = result1 * base1
i = i + 1
else:
return result1
print(raise_to_power_1(5,2))
Or even (since:
"To iterate is human, to recurse, divine")
def raise_to_power_1(base1, power1):
if ( power1 == 0):
return 1
return base1 * raise_to_power_1(base1, power1-1)
print(raise_to_power_1(5,2))