Allen question

Number Theory Level 4

$X,Y$ and $Z$ are positive integers satisfying $X^{Y^Z} = 2^8$ . Find the largest possible value of $X\times Y\times Z$ .

1 solution

Vinayak Srivastava
May 20, 2020

$X^{{Y^Z}}=2^8=256$

$\implies X^{{Y^Z}} =256$

To maximize $X \times Y \times Z$ ,

We can take $X=256, Y=1, Z=1$

Hence our answer is $X \times Y \times Z = 256\times 1 \times 1 =\boxed{256}$