1) Since we have the function:
[tex]f(x)=2^x[/tex]And a polynomial, by definition, is written as:
[tex]P(x)\text{ = }a_nx^n+.\ldots.a_0x^0[/tex]2) Then No, we can't rewrite it as a polynomial function since there are no other constants and coefficients and this exponential function is written as simple as that.