diff --git a/math/binary_exponentiation.py b/math/binary_exponentiation.py
new file mode 100644
index 0000000..aa0f165
--- /dev/null
+++ b/math/binary_exponentiation.py
@@ -0,0 +1,22 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+# author: bt3gl
+
+```
+Binary exponentiation, also known as exponentiation by squaring, is a technique for 
+efficiently computing the power of a number. By repeatedly squaring x and halving n, 
+we can quickly compute x^n using a logarithmic number of multiplications.
+````
+
+def binary_exp(x: float, n: int) -> float:
+
+  if n == 0:
+      return 1
+
+  if n < 0:
+      return 1.0 / binary_exp(x, -1 * n)
+        
+  if n % 2 == 1:
+      return x * binary_exp(x * x, (n - 1) // 2)
+        
+  return binary_exp(x * x, n // 2)