For example, the polynomial in the function $P(x) = 3x^4-2x^3+x^2+7x+8$ could be written as $3x^4-2x^3+x^2+7x^1+8x^0$, and it should mean the same thing for anything to the unary power is identical to itself and anything to the zeroeth power is equal to the unit quantity (1).
However I’m having difficulty evaluating the second case if the input is zero. For $P(x) = 3x^4-2x^3+x^2+7x+8$ = 8, but $x^0 = 0^0 = $ undefined in $3x^4-2x^3+x^2+7x^1+8x^0$.
So how is the first one defined or non-zero if the more explicit form of the polynomial is not?