diff --git a/Jint.Tests/Runtime/BigIntTests.cs b/Jint.Tests/Runtime/BigIntTests.cs
index c3ef814d8f..5ee2237571 100644
--- a/Jint.Tests/Runtime/BigIntTests.cs
+++ b/Jint.Tests/Runtime/BigIntTests.cs
@@ -1,5 +1,6 @@
 using System.Numerics;
 using Jint.Native;
+using Jint.Runtime;
 
 namespace Jint.Tests.Runtime;
 
@@ -67,4 +68,60 @@ public void ObjectIsReturnsFalseDifferentComparisonsWithBigInt(string statement)
         // Assert
         Assert.False(result.AsBoolean());
     }
+
+    [Theory]
+    [InlineData("11n ** 711111111n")]
+    [InlineData("2n ** 10000000n")]
+    [InlineData("100n ** 1000000n")]
+    public void ExponentiationShouldThrowForExcessiveSize(string expression)
+    {
+        var engine = new Engine(options =>
+        {
+            options.TimeoutInterval(TimeSpan.FromSeconds(5));
+            options.LimitMemory(16_000_000);
+        });
+
+        var ex = Assert.Throws<JavaScriptException>(() => engine.Evaluate(expression));
+        Assert.Contains("Maximum BigInt size exceeded", ex.Message);
+    }
+
+    [Theory]
+    [InlineData("11n ** 711111111n")]
+    [InlineData("2n ** 10000000n")]
+    public void ExponentiationAssignmentShouldThrowForExcessiveSize(string expression)
+    {
+        var engine = new Engine(options =>
+        {
+            options.TimeoutInterval(TimeSpan.FromSeconds(5));
+            options.LimitMemory(16_000_000);
+        });
+
+        // Convert "a ** b" to "x = a; x **= b" to test assignment path
+        var parts = expression.Split(new[] { " ** " }, StringSplitOptions.None);
+        var script = $"var x = {parts[0]}; x **= {parts[1]}; x";
+
+        var ex = Assert.Throws<JavaScriptException>(() => engine.Evaluate(script));
+        Assert.Contains("Maximum BigInt size exceeded", ex.Message);
+    }
+
+    [Theory]
+    [InlineData("2n ** 100n", "1267650600228229401496703205376")]
+    [InlineData("3n ** 50n", "717897987691852588770249")]
+    [InlineData("0n ** 1000000n", "0")]
+    [InlineData("1n ** 1000000n", "1")]
+    [InlineData("(-1n) ** 1000001n", "-1")]
+    public void ExponentiationShouldWorkForReasonableSizes(string expression, string expected)
+    {
+        var engine = new Engine();
+        var result = engine.Evaluate(expression);
+        Assert.Equal(expected, result.ToString());
+    }
+
+    [Fact]
+    public void NegativeExponentShouldThrowRangeError()
+    {
+        var engine = new Engine();
+        var ex = Assert.Throws<JavaScriptException>(() => engine.Evaluate("2n ** -1n"));
+        Assert.Contains("Exponent must be positive", ex.Message);
+    }
 }
diff --git a/Jint/Runtime/Interpreter/Expressions/JintAssignmentExpression.cs b/Jint/Runtime/Interpreter/Expressions/JintAssignmentExpression.cs
index bd2a05d187..facfc3cd75 100644
--- a/Jint/Runtime/Interpreter/Expressions/JintAssignmentExpression.cs
+++ b/Jint/Runtime/Interpreter/Expressions/JintAssignmentExpression.cs
@@ -355,11 +355,20 @@ protected override object EvaluateInternal(EvaluationContext context)
                         else
                         {
                             var exponent = TypeConverter.ToBigInt(rval);
-                            if (exponent > int.MaxValue || exponent < int.MinValue)
+                            if (exponent < 0)
                             {
-                                Throw.TypeError(context.Engine.Realm, "Cannot do exponentiation with exponent not fitting int32");
+                                Throw.RangeError(context.Engine.Realm, "Exponent must be positive");
                             }
-                            newLeftValue = JsBigInt.Create(BigInteger.Pow(TypeConverter.ToBigInt(originalLeftValue), (int) exponent));
+
+                            if (exponent > int.MaxValue)
+                            {
+                                Throw.RangeError(context.Engine.Realm, "Maximum BigInt size exceeded");
+                            }
+
+                            var intExponent = (int) exponent;
+                            var baseValue = TypeConverter.ToBigInt(originalLeftValue);
+                            JintBinaryExpression.ValidateBigIntPowSize(context.Engine.Realm, baseValue, intExponent);
+                            newLeftValue = JsBigInt.Create(BigInteger.Pow(baseValue, intExponent));
                         }
 
                         break;
diff --git a/Jint/Runtime/Interpreter/Expressions/JintBinaryExpression.cs b/Jint/Runtime/Interpreter/Expressions/JintBinaryExpression.cs
index 94b6449bc6..ab1344e8c4 100644
--- a/Jint/Runtime/Interpreter/Expressions/JintBinaryExpression.cs
+++ b/Jint/Runtime/Interpreter/Expressions/JintBinaryExpression.cs
@@ -250,6 +250,23 @@ internal static void AssertValidBigIntArithmeticOperands(JsValue left, JsValue r
         }
     }
 
+    /// <summary>
+    /// Validates that BigInteger.Pow(base, exponent) won't produce an excessively large result.
+    /// Limits result to ~1 million bits (~125 KB) to prevent memory exhaustion.
+    /// </summary>
+    internal static void ValidateBigIntPowSize(Realm realm, BigInteger baseValue, int exponent)
+    {
+        if (exponent > 0)
+        {
+            var absBase = BigInteger.Abs(baseValue);
+            if (absBase > BigInteger.One
+                && (double) exponent * BigInteger.Log(absBase, 2.0) > 1_000_000)
+            {
+                Throw.RangeError(realm, "Maximum BigInt size exceeded");
+            }
+        }
+    }
+
     private sealed class StrictlyEqualBinaryExpression : JintBinaryExpression
     {
         public StrictlyEqualBinaryExpression(NonLogicalBinaryExpression expression) : base(expression)
@@ -881,11 +898,15 @@ protected override object EvaluateInternal(EvaluationContext context)
                     Throw.RangeError(context.Engine.Realm, "Exponent must be positive");
                 }
 
-                if (exponent > int.MaxValue || exponent < int.MinValue)
+                if (exponent > int.MaxValue)
                 {
-                    Throw.TypeError(context.Engine.Realm, "Exponent does not fit 32bit range");
+                    Throw.RangeError(context.Engine.Realm, "Maximum BigInt size exceeded");
                 }
-                result = JsBigInt.Create(BigInteger.Pow(left.AsBigInt(), (int) exponent));
+
+                var intExponent = (int) exponent;
+                var baseValue = left.AsBigInt();
+                ValidateBigIntPowSize(context.Engine.Realm, baseValue, intExponent);
+                result = JsBigInt.Create(BigInteger.Pow(baseValue, intExponent));
             }
 
             return result;