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In this paper we consider the nonlinear difference equation with several delays $${(a{x}_{n+1}+b{x}_n)}^k-{\left(c{x}_n\right)}^k+\sum _{i=1}^m{p}_i\left(n\right)x_{n-{\sigma }_i}^k=0$$ where $a,b,c\in (0,\infty )$, $k=q/r,q,r$ are positive odd integers, $m$, ${\sigma }_i$ are positive integers, $\left\{p_i\left(n\right)\right\}$, $i=1,2,\cdots ,m,$ is a real sequence with $p_i\left(n\right)\ge 0$ for all large $n$, and ${lim\; inf}_{n\to \infty }{p}_i\left(n\right)=p_i<\infty$, $i=1,2,\cdots ,m$. Some sufficient conditions for the oscillation of all solutions of the above equation are obtained.