Example 2. Calculate approximately $1.08^{3.96}$.
Solution. Let $z=f(x, y)=x^{y}, x_{0}=1, y_{0}=4$; then $\Delta x=0.08, \Delta y=-0.04$.

We have: $z_{x}^{\prime}=y x^{y-1}, \quad f_{x}^{\prime}(1,4)=1, \quad z_{y}^{\prime}=x^{y} \ln x, \quad f_{y}^{\prime}(1,4)=0$, $z_{0}=f(1,4)=1$. Finally, according to the relation of point $4^{\circ}$, we get $1.08^{3.96} \approx 1+4 \cdot 0.08=1.32$