Verified answer

2^n is exponential function that grows with increasing n

much faster than n^4 which is the pollynom of degree 4.

For n<16 2^n < n^4, however for n>16 2^n > n^4.

Coefficients 10^3 and 10^-3 do not influence the rate of growth.

Hence for n large enough term .(10^3)(n^4) can be neglected

in comparison with (10^-3)(2^n), so your left side of equation

becomes (with sufficient accuracy) (10^-3)(2^n) which is O(2^n).

because n^4< 2^n for n>100