What is the smallest positive integer, other than $1$, that is both a perfect cube and a perfect fourth power?

First you need to find the least common multiply of the powers; in this case 3 and four.
lcm=3x4=12
Now, the lcm12 is the number you need to raise the next smallest positive integer so the result will a be perfect cube and a perfect fourth power.
And we also know that the next smallest positive integer after 1 is 2; therefore the number is:

and