What is the smallest positive integer, other than $1$, that is both a perfect cube and a perfect fourth power?
To be both a perfect cube and a perfect fourth power, a number must be a perfect 12th power, since 12 is the least common multiple of 3 and 4. The smallest positive integer that is a perfect 12th power, other than $1$, is $2^{12} = 4096$. 