The power of a number says how many times to use the number in a multiplication.
To find a raised to the power b we multiply a to itself, b times. That is, a^b = a * a * a * ... * a (b occurrences of a).
This operation will take O(n) time since we need to do multiplication operation exactly n times.
We can get better execution time by using a divide and conquer approach to compute power which can before up to O(log(n)).
The idea behind the algorithm is based on the fact that:
For even Y:
X^Y = X^(Y/2) * X^(Y/2)
For odd Y:
X^Y = X^(Y/2) * X^(Y/2) * X
For example
2^4 = (2 * 2) * (2 * 2) = (2^2) * (2^2)
2^5 = (2 * 2) * (2 * 2) * 2 = (2^2) * (2^2) * (2)
Time Complexity
O(log(n))