Question

$f(x,x)=x^x$ and $f\left(f\right(x,x\left)\right){=}_x{x}^x$ and on. What is the value of f(f(f(f(7,7))))) when divided by 5?

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The correct option is C 3

Given, $f(x,x)=x^x$
and $f\left\{f\right(x,x\left)\right\}=x^{x^x}$
$\therefore f\left\{f\right\{f\left\{f\right(x,x\left)\right\}\left\}\right\}=x^{x^{x^{x^x}}}$
$f\left\{f\right\{f\left\{f\right(7,7\left)\right\}\left\}\right\}=7^{7^{7^{7^7}}}$
$Rem\left[\frac{f\left\{f\right\{f\left\{f\right(7,7\left)\right\}\left\}\right\}}{5}\right]\Rightarrow Rem\left[\frac{7^{7^{7^{7^7}}}}{5}\right]\Rightarrow Rem\left[\frac{7^{(4k+3)}}{5}\right]\Rightarrow Rem\left[\frac{7^3}{5}\right]=3$