C++ Program to Find Power of Number

You can find the power of a number in C++ by using a loop to multiply the base number by itself repeatedly, like for (int i = 1; i <= exponent; i++) result *= base;.

Examples

Inputbase = 2, exponent = 3

Output8

Inputbase = 5, exponent = 0

Output1

Inputbase = 3, exponent = 4

Output81

How to Think About It

To find the power of a number, think of multiplying the base number by itself as many times as the exponent says. If the exponent is zero, the answer is always 1. Otherwise, start with 1 and multiply by the base repeatedly until you reach the exponent count.

Algorithm

1

Get the base number and exponent from the user.

2

If the exponent is zero, return 1 immediately.

3

Initialize a result variable to 1.

4

Multiply the result by the base number repeatedly, exponent times.

5

Return or print the result.

Code

cpp

#include <iostream>
using namespace std;

int main() {
    int base, exponent;
    cout << "Enter base and exponent: ";
    cin >> base >> exponent;
    int result = 1;
    for (int i = 1; i <= exponent; i++) {
        result *= base;
    }
    cout << base << "^" << exponent << " = " << result << endl;
    return 0;
}

Output

Enter base and exponent: 2 3
2^3 = 8

Dry Run

Let's trace the input base=2 and exponent=3 through the code

1

Input

base = 2, exponent = 3

2

Initialize result

result = 1

3

First loop iteration

result = 1 * 2 = 2

4

Second loop iteration

result = 2 * 2 = 4

5

Third loop iteration

result = 4 * 2 = 8

6

Output result

Print 2^3 = 8

Iteration	Result
0	1
1	2
2	4
3	8

Why This Works

Step 1: Initialize result to 1

We start with result = 1 because multiplying by 1 does not change the value and it is the identity for multiplication.

Step 2: Multiply in loop

Each loop multiplies result by base, repeating this exponent times to get the power.

Step 3: Handle zero exponent

If the exponent is zero, the loop does not run and result stays 1, which is correct since any number to the power 0 is 1.

Alternative Approaches

Using std::pow function

cpp

#include <iostream>
#include <cmath>
using namespace std;

int main() {
    double base, result;
    int exponent;
    cout << "Enter base and exponent: ";
    cin >> base >> exponent;
    result = pow(base, exponent);
    cout << base << "^" << exponent << " = " << result << endl;
    return 0;
}

This uses the built-in <code>pow</code> function from <code>cmath</code>, which is simpler but works with floating-point numbers and may introduce rounding.

Using recursion

cpp

#include <iostream>
using namespace std;

int power(int base, int exponent) {
    if (exponent == 0) return 1;
    return base * power(base, exponent - 1);
}

int main() {
    int base, exponent;
    cout << "Enter base and exponent: ";
    cin >> base >> exponent;
    cout << base << "^" << exponent << " = " << power(base, exponent) << endl;
    return 0;
}

This uses recursion to calculate power, which is elegant but can be slower and risk stack overflow for large exponents.

Complexity: O(n) time, O(1) space

Time Complexity

The loop runs exactly exponent times, so the time grows linearly with the exponent.

Space Complexity

Only a few variables are used, so space is constant O(1).

Which Approach is Fastest?

Using the built-in pow function is usually fastest and optimized, but the loop method is simple and clear for integers.

Approach	Time	Space	Best For
Loop multiplication	O(n)	O(1)	Simple integer powers
std::pow function	O(1) or optimized	O(1)	Floating-point and general use
Recursion	O(n)	O(n)	Elegant code but less efficient