We have the given permutation $$\sigma =\left({\begin{array}{*{20}c}1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9\\ 4 & 5 & 6 & 7 & 8 & 9 & 1 & 2 & 3\end{array}}\right)\ $$
Find how many solutions have the equation
$x^3=\sigma\in S_{9}$
The cycles of it are (1 4 7)(2 5 8)(3 6 9).
Can somebody help me understand how to solve it? Please!