# LeetCode 50: Powx N — Step-by-Step Visual Trace

**Medium** — Math | Recursion | Divide and Conquer

## The Problem

Implement a function to calculate x raised to the power n (x^n) efficiently. The function should handle both positive and negative exponents and return the result as a floating-point number.

## Approach

Uses fast exponentiation (exponentiation by squaring) with recursion to reduce time complexity. For negative exponents, it converts x to 1/x and makes n positive, then applies the recursive helper that squares intermediate results to minimize multiplications.

**Time:** O(log n) · **Space:** O(log n)

## Code

```python
class Solution:
    def myPow(self, x: float, n: int) -> float:
        def helper(base, exp):
            if exp == 0:
                return 1.0
            temp = helper(base, exp // 2)
            if exp % 2 == 0:
                return temp * temp
            else:
                return base * temp * temp

        if n < 0:
            x = 1 / x
            n = -n

        return helper(x, n)
```

## Watch It Run

> **[Open interactive visualization](https://tracelit.dev/app?trace=0050_powx-n)**

> **Try it yourself:** Open [TraceLit](https://tracelit.dev/app?trace=0050_powx-n) and step through every line.

---

*Built with [TraceLit](https://tracelit.dev) — the visual algorithm tracer for LeetCode practice.*