How to correctly implement the exponentiation of a polynomial?

Question

OOP

Good evening.
The problem arose such, I can not understand how to correctly raise a polynomial to a power.
This is how the polynomial is stored:

class Polynom  {
  private: 
    int deg; //степень полинома
    double *koef; //указатель на массив коэффициентов полинома

There is an overloaded multiplication operator (*) between objects, but it does not keep track of powers, i.e.
When multiplying a polynomial by a polynomial, the resulting polynomial must be initialized as

Polynom "имя объекта"(степень первого полинома умножаемого + степень второго умножаемого);

Thus, the constructor will be called to allocate memory for the required number of elements.
Constructor:

Polynom::Polynom(int count)
{
        deg=count;
        koef=new double[deg+1];
}

But I don’t understand how to implement adequate exponentiation while initializing the resulting polynomial to the required degree.
Maybe it will be possible to implement this in the exponentiation function itself.
Tell me, please, who is not difficult and understands.

Answer 1

If a polynomial of degree m is raised to a degree n, then the resulting polynomial will have degree m*n.