Power in Mathematics (original) (raw)

Last Updated : 11 Jul, 2025

The power of a number says how many times to use the number in a multiplication. Powers are also called Exponents or Indices. For example, 8^2 could be called "8 to the power 2" or "8 to the second power", or simply "8 squared".

Some interesting fact about Power :

  1. If the indices is 1, then you just have the number itself. For example, 5^1 = 5
  2. If the indices is 0, then you get 1. For example, 5^0 = 1
  3. Exponents make it easier to write and use many multiplications
  4. Negative exponent means how many times to divide one by the number.For example, 5^-1 = 1 /5 = 0.2

How we check if a number is power of y for a given integer x ?
Naive solution:
Given two positive numbers x and y, check if y is a power of x or not.
Examples :

Input: x = 10, y = 1 Output: True

Input: x = 10, y = 1000 Output: True

Input: x = 10, y = 1001 Output: False

Approach : A simple solution is to repeatedly compute powers of x. If a power becomes equal to y, then y is a power, else not.

C++ `

// C++ program to check if a number is power of // another number #include <bits/stdc++.h> using namespace std;

/* Returns 1 if y is a power of x */ bool isPower(int x, long int y) { // The only power of 1 is 1 itself if (x == 1) return (y == 1);

// Repeatedly compute power of x
long int pow = 1;
while (pow < y)
    pow *= x;

// Check if power of x becomes y
return (pow == y);

}

/* Driver program to test above function */ int main() { cout << (isPower(10, 1) ? "True" : "False") << endl; cout << (isPower(1, 20) ? "True" : "False") << endl; cout << (isPower(2, 128) ? "True" : "False") << endl; cout << (isPower(2, 30) ? "True" : "False") << endl; return 0; }

Java

// Java program to check if a number is power of // another number public class Test {

// driver method to test power method
public static void main(String[] args)
{
    // check the result for true/false and print.
    System.out.println(isPower(10, 1) ? "True" : "False");
    System.out.println(isPower(1, 20) ? "True" : "False");
    System.out.println(isPower(2, 128) ? "True" : "False");
    System.out.println(isPower(2, 30) ? "True" : "False");
}

/* Returns true if y is a power of x */
public static boolean isPower(int x, int y)
{
    // The only power of 1 is 1 itself
    if (x == 1)
        return (y == 1);

    // Repeatedly compute power of x
    int pow = 1;
    while (pow < y)
        pow = pow * x;

    // Check if power of x becomes y
    return (pow == y);
}

}

Python3

Python program to check

if a number is power of

another number

Returns true if y is a

power of x

def isPower (x, y):

# The only power of 1
# is 1 itself
if (x == 1):
    return (y == 1)
    
# Repeatedly compute
# power of x
pow = 1
while (pow < y):
    pow = pow * x

# Check if power of x
# becomes y
return (pow == y)

Driver Code

check the result for

true/false and print.

if(isPower(10, 1)): print("True") else: print("False")

if(isPower(1, 20)): print("True") else: print("False")

if(isPower(2, 128)): print("True") else: print("False")

if(isPower(2, 30)): print("True") else: print("False")

C#

// C# program to check if a number // is power of another number using System;

class GFG {

// Returns true if y is a power of x 
public static bool isPower (int x, int y)
{
    // The only power of 1 is 1 itself
    if (x == 1)
    return (y == 1);

    // Repeatedly compute power of x
    int pow = 1;
    while (pow < y)
    pow = pow * x;

    // Check if power of x becomes y
    return (pow == y);
}

// Driver Code
public static void Main ()
{
    //check the result for true/false and print.
    Console.WriteLine(isPower(10, 1) ? "True" : "False");
    Console.WriteLine(isPower(1, 20) ? "True" : "False");
    Console.WriteLine(isPower(2, 128) ? "True" : "False");
    Console.WriteLine(isPower(2, 30) ? "True" : "False");
}

}

PHP

pow∗=pow *= pow∗=x; // Check if power of x becomes y return ($pow == $y ? "True" : "False"); } // Driver Code echo isPower(10, 1) . "\n"; echo isPower(1, 20) . "\n"; echo isPower(2, 128) . "\n"; echo isPower(2, 30) . "\n"; ?>

JavaScript

`

Output:

True False True False

Time complexity of above solution is O(Logxy)

Auxiliary Space: O(1)
Basic Program related to Power :

More problems related to Powers :

Recent Articles on Power!