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# Math

## Q1: [Pow(x, n)](https://leetcode.com/problems/powx-n/)

```cpp
class Solution {
public:
    double myPow(double x, long int n) {
        long int N;
        if (n < 0) {
            N = -(long)n;
            return 1.0 / sol(x, N);
        }
        return sol(x, n);
    }

    double sol(double x, long int n) {
        if(n == 0) return 1;
        else if(n == 1) return x;
        else if(n%4 == 0) {
            double y = sol(x, n/4);
            return y*y*y*y;
        }
        else if(n%2 == 0) {
            double y = sol(x, n/2);
            return y*y;
        }
        else {
            double y = sol(x, (n-1)/2);
            return y*y*x;
        }
     }
};
```

## Q2: [Multiply Strings](https://leetcode.com/problems/multiply-strings/)

```cpp
class Solution {
public:
    
    string multiply(string num1, string num2) {
        if(num1[0] == '0' || num2[0] == '0') return "0";

        string sum(num1.size() + num2.size(), '0');
    
        for (int i = num1.size() - 1; i >= 0; i--) {
            int carry = 0;
            for (int j = num2.size() - 1; j >= 0; j--) {
                int temp = (sum[i + j + 1] - '0') + (num1[i] - '0') * (num2[j] - '0') + carry;
                sum[i + j + 1] = temp % 10 + '0';
                carry = temp / 10;
            }
            sum[i] += carry;
        }
        
        int i = 0;
        while(sum[i] == '0') i++; // removing prefix zeroes
        
        string res = "";
        for(i; i < sum.size(); i++) res += sum[i];
        
        return res;
    }
};
```