diff --git a/src/property_utils/properties/property.py b/src/property_utils/properties/property.py
index 92d77f6..d3904e0 100644
--- a/src/property_utils/properties/property.py
+++ b/src/property_utils/properties/property.py
@@ -217,7 +217,7 @@ def __mul__(self, other) -> "Property":
         if isinstance(other, Property):
             _other = self._unit_preconversion(other)
             return Property(
-                self.value * _other.value, (self.unit * _other.unit).simplified()
+                self.value * _other.value, self._simplify_units(self.unit * _other.unit)
             )
         raise PropertyBinaryOperationError(
             f"cannot multiply {self} with {other}; "
@@ -268,7 +268,7 @@ def __truediv__(self, other) -> "Property":
                 raise PropertyBinaryOperationError(
                     f"cannot divide {self} with {other}; denominator's value is zero. "
                 ) from None
-            return Property(value, (self.unit / _other.unit).simplified())
+            return Property(value, self._simplify_units(self.unit / _other.unit))
         raise PropertyBinaryOperationError(
             f"cannot divide {self} with {other}; "
             "denominator must be numeric or Property. "
@@ -299,7 +299,7 @@ def __rtruediv__(self, other) -> "Property":
                 raise PropertyBinaryOperationError(
                     f"cannot divide {self} with {other}; denominator's value is zero. "
                 ) from None
-            return Property(value, (other.unit / self.unit).simplified())
+            return Property(value, self._simplify_units(other.unit / self.unit))
         raise PropertyBinaryOperationError(
             f"cannot divide {self} with {other}; "
             "numerator must be numeric or Property. "
@@ -727,3 +727,15 @@ def _simple_unit_preconversion(self, unit: MeasurementUnit) -> MeasurementUnit:
         multiplication or division with this property.
         """
         return self._dimension_unit_preconversion(unit**1).unit
+
+    def _simplify_units(self, unit: CompositeDimension) -> UnitDescriptor:
+        """
+        Simplifies the composite dimension and returns NON_DIMENSIONAL if the simplified
+        composite does not have units.
+        """
+        unit = unit.simplified()
+
+        if unit.has_no_units():
+            return NonDimensionalUnit.NON_DIMENSIONAL
+        
+        return unit
diff --git a/src/property_utils/tests/properties/test_property.py b/src/property_utils/tests/properties/test_property.py
index 079c1e5..93cc319 100644
--- a/src/property_utils/tests/properties/test_property.py
+++ b/src/property_utils/tests/properties/test_property.py
@@ -346,6 +346,10 @@ def test_with_exponentiated_property(self):
     def test_with_inverse_property(self):
         self.assert_result("10.4 ")
 
+    @args({"other": Property(2, Unit1.A ** (-1))})
+    def test_produced_units_with_inverse_property(self):
+        self.assertEqual(self.result().unit, NonDimensionalUnit.NON_DIMENSIONAL)
+
     @args({"other": Property(4, Unit2.B)})
     def test_with_other_propperty(self):
         self.assert_result("20.8 A * B")
@@ -499,6 +503,10 @@ def test_with_exponentiated_property(self):
     def test_with_same_property(self):
         self.assert_result("3.0 ")
 
+    @args({"other": Property(2, Unit1.A)})
+    def test_produced_units_with_same_property(self):
+        self.assertEqual(self.result().unit, NonDimensionalUnit.NON_DIMENSIONAL)
+
     @args({"other": Property(2, Unit2.B)})
     def test_with_other_propperty(self):
         self.assert_result("3.0 A / B")
@@ -639,6 +647,10 @@ def test_with_exponentiated_property(self):
     def test_with_same_property(self):
         self.assert_result("0.2 ")
 
+    @args({"other": Property(2, Unit1.A)})
+    def test_produced_units_with_same_property(self):
+        self.assertEqual(self.result().unit, NonDimensionalUnit.NON_DIMENSIONAL)
+
     @args({"other": Property(2, Unit2.B)})
     def test_with_other_propperty(self):
         self.assert_result("0.2 B / A")