diff --git a/Algebra-and-Numerical-Methods/FastExponentiation.cpp b/Algebra-and-Numerical-Methods/FastExponentiation.cpp
new file mode 100644
index 0000000..0f01d39
--- /dev/null
+++ b/Algebra-and-Numerical-Methods/FastExponentiation.cpp
@@ -0,0 +1,31 @@
+//Calculates a^b
+//Time Complexity - log(b), Space Complexity - O(1)
+
+#include <bits/stdc++.h>
+#define int long long
+using namespace std;
+int mod = 1e9+7;
+
+int fastModExponentiation(int a, int b)
+{
+    int ans=1;
+    while(b>0)
+    {
+        if(b&1){
+            ans=(ans*a)%mod;
+        }
+        b=b>>1;
+        a=(a*a)%mod;
+    }
+    return ans;
+}
+
+signed main()
+{
+    cin.tie(NULL);
+    cout.tie(NULL);
+    int a, b;
+    cin>>a>>b;
+    cout<<fastModExponentiation(a,b);
+    return 0;
+}