For how many positive integers n>1 is it true that \(2^{42}\) is a perfect nth power?
+2666 For any positive integer to satisfy the conditions, it has to be a perfect power of \(2\), and it should be able to be equivalent to \(2^{42}\), with integer values.
The only possible options are:
\(2\), can be written as \(2^{42}\)
\(4\), can be written as \(({2^2)}^{21}\)
\(8\), can be written as \((2^3)^{14}\)
Thus... the answer is \(\color{brown}\boxed3\)
