نکته: با فرض $K\in \mathbb{Z}$ داریم: $\left[ X \right]=K\Leftrightarrow K\le X\lt K+1$  $\left\{ \begin{matrix} 0\lt \frac{37}{41}\lt 1\Rightarrow 0\lt {{(\frac{37}{41})}^{3}}\lt 1\Rightarrow \left[ {{(\frac{37}{41})}^{3}} \right]=0  \\ -1\lt \frac{-13}{51}\lt 0\Rightarrow -1\lt {{(\frac{-13}{51})}^{5}}\lt 0\Rightarrow \left[ {{(\frac{-13}{51})}^{{}}} \right]=-1  \\ \end{matrix} \right.\Rightarrow \left[ {{(\frac{37}{41})}^{3}} \right]+\left[ {{(\frac{-13}{51})}^{5}} \right]=0+(-1)=-1$