find the values of

Question:

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

(i) $\left(a^{b}+b^{a}\right)^{-1}$

(ii) $\left(a^{a}+b^{b}\right)^{-1}$

 

Solution:

(i) $\left(a^{b}+b^{a}\right)^{-1}$

$\left(a^{b}+b^{a}\right)^{-1}=\left(2^{3}+3^{2}\right)^{-1}$

$=(8+9)^{-1}$

$=(17)^{-1}$

$=\frac{1}{17}$

(ii) $\left(a^{a}+b^{b}\right)^{-1}$

$\left(a^{a}+b^{b}\right)^{-1}=\left(2^{2}+3^{3}\right)^{-1}$

$=(4+27)^{-1}$

$=(31)^{-1}$

$=\frac{1}{31}$

 

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