This program checks whether a number n can be expressed as power of k and if yes, then to what power should k be raised to make it n. Following example will clarify :

**Examples:**

Input : n = 16, k = 2 Output : yes : 4 Explanation : Answer is yes because 16 can be expressed as power of 2. Input : n = 27, k = 3 Output : yes : 3 Explanation : Answer is yes as 27 can be expressed as power of 3. Input : n = 20, k = 5 Output : No Explanation : Answer is No as 20 cannot be expressed as power of 5.

We have discussed two methods in below post

:Check if a number is a power of another number

In this post, a new Base Changing method is discussed.

In **Base Changing Method**, we simply change the base of number n to k and check if the first digit of Changed number is 1 and remaining all are zero.

**Example for this** : Let’s take n = 16 and k = 2.

Change 16 to base 2. i.e. (10000)_{2}. Since first digit is 1 and remaining are zero. Hence 16 can be expressed as power of 2. Count the length of (10000)_{2} and subtract 1 from it, that’ll be the number to which 2 must be raised to make 16. In this case 5 – 1 = 4.

**Another example** : Let’s take n = 20 and k = 3.

20 in base 3 is (202)_{3}. Since there are two non-zero digit, hence 20 cannot be expressed as power of 3.

// CPP program to check if a number can be // raised to k #include <iostream> #include <algorithm> using namespace std; bool isPowerOfK(unsigned int n, unsigned int k) { // loop to change base n to base = k bool oneSeen = false; while (n > 0) { // Find current digit in base k int digit = n % k; // If digit is neither 0 nor 1 if (digit > 1) return false; // Make sure that only one 1 // is present. if (digit == 1) { if (oneSeen) return false; oneSeen = true; } n /= k; } return true; } // Driver code int main() { int n = 64, k = 4; if (isPowerOfK(n ,k)) cout << "Yes"; else cout << "No"; }

Output:

Yes

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