$6.(4$ points$)$ Consider the following Python function, which recursively computes the value of $\backslash ($ a$^\{$b$\}\backslash ).$ Assume that $\backslash ($ b $\backslash )$ is a non$-$negative integer.

$```$

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

if b $==0$:

return $1$

else

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

$```$

Use induction to prove that this algorithm is correct.