If $a = 3$ and $b =-2$, find the values of:$a^b + b^a$

Given:

$a = 3$ and $b =-2$

To do:

We have to find the value of $a^b+ b^a$.

Solution:

We know that,

$a^{-m}=\frac{1}{a^m}$

Therefore,

$a^b+ b^a=(3)^{-2}+(-2)^{3}$

$=\frac{1}{(-3)^{2}}+(-8)$

$=\frac{1}{9}-8$

$=\frac{1-8\times9}{9}$

$=\frac{1-72}{9}$

$=\frac{-71}{9}$

Hence, $a^b+b^a=\frac{-71}{9}$.