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

Question:

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

(i) $a^{a}+b^{b}$

(ii) $a^{b}+b^{a}$

(iii) $a^{b}+b^{a}$

Solution:

(i) We have,

$a^{a}+b^{b}$

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

$=3^{3}+(-1 / 2)^{2}$

$=27+1 / 4$

$=109 / 4$

(ii) $a^{b}+b^{a}$

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

$=(1 / 3)^{2}+(-2)^{3}$

$=1 / 9-8$

$=-(71 / 9)$

(iii) We have, 

$a^{b}+b^{a}$

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

$=(3-2))^{-6}$

$=1^{-6}=1$

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