Question

If $x=2$ and $y=3$, then find the value of $\left[\frac{1}{x^x}+\frac{1}{y^y}\right]$.

• A. $\frac{-31}{108}$
• B. $\frac{31}{108}$
• C. $\frac{125}{171}$
• D. $\frac{153}{222}$

Answer 1

The correct option is B $\frac{31}{108}$

$\frac{1}{x^x}+\frac{1}{y^y}=\frac{1}{2^2}+\frac{1}{3^3}$

$=\frac{1}{4}+\frac{1}{27}=\frac{27+4}{108}$

$=\frac{31}{108}$