Power in Mathematics

06 Jul, 2022
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 :  
If the indices is 1, then you just have the number itself. For example, 5^1 = 5If the indices is 0, then you get 1. For example, 5^0 = 1Exponents make it easier to write and use many multiplicationsNegative exponent means how many times to divide one by the number.For example, 5^-1 = 1 /5 = 0.2
If the indices is 1, then you just have the number itself. For example, 5^1 = 5
If the indices is 0, then you get 1. For example, 5^0 = 1
Exponents make it easier to write and use many multiplications
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++
Java
Python3
C#
PHP
Javascript
// 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 comput 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 program to check if a number is power of// another numberpublic 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);    }}
# Python program to check# if a number is power of# another number # Returns true if y is a# power of xdef 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# program to check if a number// is power of another numberusing 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// PHP program to check if a// number is power of another number /* Returns 1 if y is a power of x */function isPower($x, $y){    // The only power of 1 is 1 itself    if ($x == 1)        return ($y == 1 ? "True" : "False");     // Repeatedly comput power of x    $pow = 1;    while ($pow < $y)        $pow *= $x;     // Check if power of x becomes y    return ($pow == $y ? "True" : "False");} // Driver Codeecho isPower(10, 1) . "\n";echo isPower(1, 20) . "\n";echo isPower(2, 128) . "\n";echo isPower(2, 30) . "\n"; ?>
<script> // Javascript program to check if a number is power of// another number  /* Returns 1 if y is a power of x */function isPower( x, y){    // The only power of 1 is 1 itself    if (x == 1)        return (y == 1);     // Repeatedly comput power of x    let  pow = 1;    while (pow < y)        pow *= x;     // Check if power of x becomes y    return (pow == y);}      // Driver Code         document.write((isPower(10, 1) ? "True" : "False") + "</br>");    document.write((isPower(1, 20) ? "True" : "False") + "</br>");    document.write((isPower(2, 128) ? "True" : "False") + "</br>");    document.write((isPower(2, 30) ? "True" : "False") + "</br>");     </script>
Output:  
True
False
True
False
Time complexity of above solution is O(Logxy)
Auxiliary Space: O(1)Basic Program related to Power :  
Find unit digit of x raised to power y
Check if a number can be expressed as x^y (x raised to power y)
Find the multiple of x which is closest to a^b
All possible numbers of N digits and base B without leading zeros
Check if a number can be expressed as a^b | Set 2
Write you own Power without using multiplication(*) and division(/) operators
More problems related to Powers :  
Total number of subsets in which the product of the elements is even
Sum of first N natural numbers which are not powers of K
GCD of a number raised to some power and another number
Largest N digit number divisible by given three numbers
Check whether a given Number is Power-Isolated or not
Recent Articles on Power!  
jana_sayantan
subham348
maths-power
Mathematical
School Programming
Mathematical
Writing code in comment?
Please use ide.geeksforgeeks.org,
generate link and share the link here.
Algorithm to solve Rubik's Cube
Merge two sorted arrays with O(1) extra space
Program to print prime numbers from 1 to N.
Find next greater number with same set of digits
Segment Tree | Set 1 (Sum of given range)
Python Dictionary
Reverse a string in Java
Arrays in C/C++
Introduction To PYTHON
Interfaces in Java