f(x)=x^5+4x^4-4x^3-16x^2 h(x)=2^x (f*h)(x)= ?

Substitute 2^x into f(x)=f(2^x)=(f of h):

(2^x)^5+4(2^x)^4-4(2^x)^3-16(2^x)^2=

2^(5x)+2^(4x+2)-2^(3x+2)-2^(2x+4).

This can be written: (2^(2x))(2^3x+2^(2(x+1))-2^(x+2)-16).