Question

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

(i) (a^b + b^a)^–1

(ii) (a^a + b^b)^–1

Answer 1

(i) (a^b + b^a)^–1
$$\begin{gathered} {\left(a^b+b^a\right)}^{-1}={\left(2^3+3^2\right)}^{-1} \\ ={\left(8+9\right)}^{-1} \\ ={\left(17\right)}^{-1} \\ =\frac{1}{17} \end{gathered}$$



(ii) (a^a + b^b)^–1
$$\begin{gathered} {\left(a^a+b^b\right)}^{-1}={\left(2^2+3^3\right)}^{-1} \\ ={\left(4+27\right)}^{-1} \\ ={\left(31\right)}^{-1} \\ =\frac{1}{31} \end{gathered}$$