Power in Mathematics

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". 
 

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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. 
 

Output: 
 

True
False
True
False

Time complexity of above solution is O(Log_xy)

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

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