Question

If a = 1, b = 2 then find the value of (a^b + b^a)^–1.

Answer 1

For a = 1and b = 2,
$$\begin{gathered} {\left(a^b+b^a\right)}^{-1} \\ ={\left(1^2+2^1\right)}^{-1} \\ ={\left(1+2\right)}^{-1} \end{gathered}$$
$$\begin{gathered} =3^{-1} \\ =\frac{1}{3}\left(x^{-a}=\frac{1}{x^a}\right) \end{gathered}$$
Thus, the value of (a^b + b^a)^–1 when a = 1 and b = 2 is $\frac{1}{3}$.