diff --git a/crates/oxc_transformer/src/es2016/exponentiation_operator.rs b/crates/oxc_transformer/src/es2016/exponentiation_operator.rs
index 3576b775f..4e94db22e 100644
--- a/crates/oxc_transformer/src/es2016/exponentiation_operator.rs
+++ b/crates/oxc_transformer/src/es2016/exponentiation_operator.rs
@@ -78,17 +78,18 @@ impl<'a, 'ctx> Traverse<'a> for ExponentiationOperator<'a, 'ctx> {
                     AssignmentTarget::AssignmentTargetIdentifier(_) => {
                         self.convert_identifier_assignment(expr, ctx);
                     }
-                    // Note: We do not match `AssignmentTarget::PrivateFieldExpression` here.
-                    // From Babel: "We can't generate property ref for private name, please install
-                    // `@babel/plugin-transform-class-properties`".
-                    // TODO: Ensure this plugin interacts correctly with class private properties
-                    // transform, so the property is transformed before this transform.
                     AssignmentTarget::StaticMemberExpression(_) => {
                         self.convert_static_member_expression_assignment(expr, ctx);
                     }
                     AssignmentTarget::ComputedMemberExpression(_) => {
                         self.convert_computed_member_expression_assignment(expr, ctx);
                     }
+                    // Babel refuses to transform this: "We can't generate property ref for private name,
+                    // please install `@babel/plugin-transform-class-properties`".
+                    // But there's no reason not to.
+                    AssignmentTarget::PrivateFieldExpression(_) => {
+                        self.convert_private_field_assignment(expr, ctx);
+                    }
                     _ => {}
                 }
             }
@@ -364,6 +365,82 @@ impl<'a, 'ctx> ExponentiationOperator<'a, 'ctx> {
         (pow_left, temp_var_inits)
     }
 
+    /// Convert `AssignmentExpression` where assignee is a private field member expression.
+    ///
+    /// `obj.#prop **= right` transformed to:
+    /// * If `obj` is a bound symbol:
+    ///   -> `obj.#prop = Math.pow(obj.#prop, right)`
+    /// * If `obj` is unbound:
+    ///   -> `var _obj; _obj = obj, _obj.#prop = Math.pow(_obj.#prop, right)`
+    ///
+    /// `obj.foo.bar.#qux **= right` transformed to:
+    /// ```js
+    /// var _obj$foo$bar;
+    /// _obj$foo$bar = obj.foo.bar, _obj$foo$bar.#qux = Math.pow(_obj$foo$bar.#qux, right)
+    /// ```
+    ///
+    /// Temporary variable is to avoid side-effects of getting `obj` / `obj.foo.bar` being run twice.
+    //
+    // `#[inline]` so compiler knows `expr` is an `AssignmentExpression` with `PrivateFieldExpression` on left
+    #[inline]
+    fn convert_private_field_assignment(
+        &mut self,
+        expr: &mut Expression<'a>,
+        ctx: &mut TraverseCtx<'a>,
+    ) {
+        let Expression::AssignmentExpression(assign_expr) = expr else { unreachable!() };
+        let AssignmentTarget::PrivateFieldExpression(member_expr) = &mut assign_expr.left else {
+            unreachable!()
+        };
+
+        let (pow_left, temp_var_inits) = self.get_pow_left_private_field(member_expr, ctx);
+        Self::convert_assignment(assign_expr, pow_left, ctx);
+        Self::revise_expression(expr, temp_var_inits, ctx);
+    }
+
+    /// Get left side of `Math.pow(pow_left, ...)` for static member expression
+    /// and replacement for left side of assignment.
+    fn get_pow_left_private_field(
+        &mut self,
+        field_expr: &mut PrivateFieldExpression<'a>,
+        ctx: &mut TraverseCtx<'a>,
+    ) -> (
+        // Left side of `Math.pow(pow_left, ...)`
+        Expression<'a>,
+        // Temporary var initializations
+        Vec<'a, Expression<'a>>,
+    ) {
+        // Object part of 2nd member expression
+        // ```
+        // obj.#prop = Math.pow(obj.#prop, right)
+        //                      ^^^
+        // ```
+        let mut temp_var_inits = ctx.ast.vec();
+        let obj = self.get_second_member_expression_object(
+            &mut field_expr.object,
+            &mut temp_var_inits,
+            ctx,
+        );
+
+        // Property part of 2nd member expression
+        // ```
+        // obj.#prop = Math.pow(obj.#prop, right)
+        //                          ^^^^^
+        // ```
+        let field = field_expr.field.clone_in(ctx.ast.allocator);
+
+        // Complete 2nd member expression
+        // ```
+        // obj.#prop = Math.pow(obj.#prop, right)
+        //                      ^^^^^^^^^
+        // ```
+        let pow_left = Expression::from(
+            ctx.ast.member_expression_private_field_expression(SPAN, obj, field, false),
+        );
+
+        (pow_left, temp_var_inits)
+    }
+
     /// Get object part of 2nd member expression to be used as `left` in `Math.pow(left, right)`.
     ///
     /// Also update the original `obj` passed in to function, and add a temp var initializer, if necessary.
diff --git a/tasks/transform_conformance/tests/babel-plugin-transform-exponentiation-operator/test/fixtures/bail-private-properties/input.js b/tasks/transform_conformance/tests/babel-plugin-transform-exponentiation-operator/test/fixtures/bail-private-properties/input.js
deleted file mode 100644
index b61b2daf9..000000000
--- a/tasks/transform_conformance/tests/babel-plugin-transform-exponentiation-operator/test/fixtures/bail-private-properties/input.js
+++ /dev/null
@@ -1,9 +0,0 @@
-class C {
-    #p = 1;
-
-    method(obj) {
-        obj.x **= 2; // Transform
-        obj['y'] **= 3; // Transform
-        obj.#p **= 4; // Bail
-    }
-}
diff --git a/tasks/transform_conformance/tests/babel-plugin-transform-exponentiation-operator/test/fixtures/bail-private-properties/output.js b/tasks/transform_conformance/tests/babel-plugin-transform-exponentiation-operator/test/fixtures/bail-private-properties/output.js
deleted file mode 100644
index def6e695e..000000000
--- a/tasks/transform_conformance/tests/babel-plugin-transform-exponentiation-operator/test/fixtures/bail-private-properties/output.js
+++ /dev/null
@@ -1,9 +0,0 @@
-class C {
-    #p = 1;
-
-    method(obj) {
-        obj["x"] = Math.pow(obj["x"], 2);
-        obj["y"] = Math.pow(obj["y"], 3);
-        obj.#p **= 4;
-    }
-}
diff --git a/tasks/transform_conformance/tests/babel-plugin-transform-exponentiation-operator/test/fixtures/private-properties/input.js b/tasks/transform_conformance/tests/babel-plugin-transform-exponentiation-operator/test/fixtures/private-properties/input.js
new file mode 100644
index 000000000..edd5e6d50
--- /dev/null
+++ b/tasks/transform_conformance/tests/babel-plugin-transform-exponentiation-operator/test/fixtures/private-properties/input.js
@@ -0,0 +1,11 @@
+class C {
+    #p = 1;
+
+    method(obj) {
+        this.#p **= 1;
+        obj.#p **= 2;
+        this.x.y.z.#p **= 3;
+        obj.x.y.z.#p **= 4;
+        fn().x.y.z.#p **= 5;
+    }
+}
diff --git a/tasks/transform_conformance/tests/babel-plugin-transform-exponentiation-operator/test/fixtures/private-properties/output.js b/tasks/transform_conformance/tests/babel-plugin-transform-exponentiation-operator/test/fixtures/private-properties/output.js
new file mode 100644
index 000000000..6ea277ca6
--- /dev/null
+++ b/tasks/transform_conformance/tests/babel-plugin-transform-exponentiation-operator/test/fixtures/private-properties/output.js
@@ -0,0 +1,12 @@
+class C {
+    #p = 1;
+
+    method(obj) {
+        var _this, _this$x$y$z, _obj$x$y$z, _fn$x$y$z;
+        _this = this, _this.#p = Math.pow(_this.#p, 1);
+        obj.#p = Math.pow(obj.#p, 2);
+        _this$x$y$z = this.x.y.z, _this$x$y$z.#p = Math.pow(_this$x$y$z.#p, 3);
+        _obj$x$y$z = obj.x.y.z, _obj$x$y$z.#p = Math.pow(_obj$x$y$z.#p, 4);
+        _fn$x$y$z = fn().x.y.z, _fn$x$y$z.#p = Math.pow(_fn$x$y$z.#p, 5);
+    }
+}