simplyfying roots

#include <iostream>
#include <vector>
#include <math.h>
#include <utility>
#include <algorithm>

using namespace std;

class Root
{
private:
    std::vector<pair<unsigned int, unsigned int>> base;
    unsigned int root;
    unsigned int multipliquer;
    unsigned int root_degree;

    void simplyfy();

public:
    Root(unsigned int root, unsigned int root_degree = 2)
        : root(root), root_degree(root_degree)
    {
        unsigned int max = pow(4294967294, 1.0/static_cast<double>(root_degree));
        for(unsigned int i = 2; i < max; i++)
            base.push_back(make_pair(i, pow(i, root_degree)));

        std::reverse(base.begin(), base.end());

        multipliquer = 0;
        this -> simplyfy();
    }

    void result();
};

void Root::simplyfy()
{
    for(int i = 0; i < 3; i++)
    {
        for(auto x: base)
            if( root == x.second )
            {
                root = 1;
                multipliquer += x.first;
                return;
            }

        for(auto x: base)
            if( root > 1 && root % x.second == 0 )
            {
                root /= x.second;
                multipliquer += x.first;
            }
    }
}

void Root::result()
{
    if ( multipliquer == 0 )
        cout << root_degree << "th degree root of " << root << "\n";
    else if ( root == 1 )
        cout << multipliquer << "\n";
    else
        cout << multipliquer << " * root(" << root << ") (" << root_degree << "th degree)\n";
}

int main()
{
    unsigned int root, root_degree;
    while(cin >> root >> root_degree)
    {
        Root* x = new Root(root, root_degree);
        x -> result();
        cout << "\n\n>";
        delete x;
    }

    return 0;
}