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\end{itemize}  \end{Exercise}  Since we can multiply polynomials in $x,y$, $x,y,z$,  we can raise them at a power $m$ as well, with the usual meaning. any power.  \\  If, for example, we take the polynomial $f(x,y,z)=x^3z+y+z+1\in $f=x^3z+y+z+1\in  \Fb[x,y,z]$, we have that $$f(x,y,z)^2=(x^3z+y+z+1)^2=f(x,y,z)f(x,y,z)=(x^3z+y+z+1)(x^3z+y+z+1)$$ $$f^2=(x^3z+y+z+1)^2=f\cdot f=(x^3z+y+z+1)(x^3z+y+z+1)$$  $$x^6z^2+y^2+z^2+1 = (x^3z)^2+(y)^2+(z)^2+1^2.$$  As in the univariate case, raising a multivariate polynomial in $\Fb[x,y,z]$ to the power 2 is the same  as raising to the power 2 its monomials and summing them.  \\  Now \underline{Now  we are ready to tackle the generic case of $n$ variables. variables.}