Which of these functions is a recursive program that correctly calculates the power of a number raised to another $($a$^$b$)?$

a$.$

def power$($a$,$b$)$:

if b $==1$:

return a

else:

return a$*$power$($b$-1,$a$)$

b$.$

def power$($a$,$b$)$:

if b $==1$:

return a

else:

return a$*$power$($a$,$b$-1)$

c$.$

def power$($a$,$b$)$:

if b $==1$:

return a

else:

return a$**$power$($a$,$b$-1)$

d$.$

None of these

e$.$

def power$($a$,$b$)$:

if b $==1$:

return a

else:

return a$**$power$($b$-1,$a$)$

f$.$

def power$($a$,$b$)$:

sm $=1$

for i in range$($b$)$:

sm$*=$a

return sm