Number systems — Maths STD 9 — Question

 We have to find the value of $\Big(\frac{\text{x}}{\text{y}}\Big)^{\text{x}-\text{y}}+\Big(\frac{\text{y}}{\text{x}}\Big)^{\text{y}-\text{x}}$ if $x = 2, y = 4$
Substitute $x = 2, y = 4,$ in $\Big(\frac{\text{x}}{\text{y}}\Big)^{\text{x}-\text{y}}+\Big(\frac{\text{y}}{\text{x}}\Big)^{\text{y}-\text{x}}$ to get,
$\Big(\frac{\text{x}}{\text{y}}\Big)^{\text{x}-\text{y}}+\Big(\frac{\text{y}}{\text{x}}\Big)^{\text{y}-\text{x}}$
$=\Big(\frac{2}{4}\Big)^{2-4}+\Big(\frac{4}{2}\Big)^{4-2}$
$=\Big(\frac{2}{4}\Big)^{-2}+\Big(\frac{4}{2}\Big)^{2}$
$=\Big(\frac{1}{2}\Big)^{-2}+(2)^2$
$=\Big(\frac{1}{2^{-2}}\Big)+4$
$\Big(\frac{\text{x}}{\text{y}}\Big)^{\text{x}-\text{y}}+\Big(\frac{\text{y}}{\text{x}}\Big)^{\text{y}-\text{x}}$
$=\frac{1}{\frac{1}{2^2}}+4$
$=\frac{1}{\frac{1}{4}}+4$
$=1\times\frac{4}{1}+4$
$=4+4$
$=8$
Hence the correct choice is $b.$