diff --git a/src/include/units/bits/tools.h b/src/include/units/bits/tools.h
index 3bf4e09e..78235793 100644
--- a/src/include/units/bits/tools.h
+++ b/src/include/units/bits/tools.h
@@ -26,6 +26,16 @@
 #include <ratio>
 #include <type_traits>
 
+namespace std {
+
+  template<typename T>
+  struct type_identity { using type = T; };
+
+  template<typename T>
+  using type_identity_t = typename type_identity<T>::type;
+
+}
+
 namespace units {
 
   using namespace mp::std_concepts;  // todo Remove when std::concepts will arrive
diff --git a/src/include/units/dimension.h b/src/include/units/dimension.h
index 10dfb44e..e9b4f4b4 100644
--- a/src/include/units/dimension.h
+++ b/src/include/units/dimension.h
@@ -78,10 +78,18 @@ namespace units {
   template<Exponent E>
   using exp_invert_t = typename exp_invert<E>::type;
 
+  // dimension_traits
+
+  template<typename T>
+  struct dimension_traits : std::type_identity<T> {};
+
+  template<typename T>
+  using dimension_traits_t = typename dimension_traits<T>::type;
+
   // dimension
 
   template<Exponent... Es>
-  struct dimension;
+  struct dimension : std::type_identity<dimension<Es...>> {};
 
   // is_dimension
   namespace detail {
@@ -93,7 +101,20 @@ namespace units {
   }  // namespace detail
 
   template<typename T>
-  concept bool Dimension = detail::is_dimension<T>;
+  concept bool Dimension = detail::is_dimension<typename T::type>;
+
+
+  // dim_invert
+
+  template<Dimension E>
+  struct dim_invert;
+
+  template<Exponent... Es>
+  struct dim_invert<dimension<Es...>> : std::type_identity<dimension_traits_t<dimension<exp_invert_t<Es>...>>> {};
+
+  template<Dimension D>
+  using dim_invert_t = typename dim_invert<typename D::type>::type;
+
 
   // make_dimension
 
@@ -144,12 +165,10 @@ namespace units {
   struct dimension_multiply;
 
   template<Exponent... E1, Exponent... E2>
-  struct dimension_multiply<dimension<E1...>, dimension<E2...>> {
-    using type = make_dimension_t<E1..., E2...>;
-  };
+  struct dimension_multiply<dimension<E1...>, dimension<E2...>> : std::type_identity<dimension_traits_t<make_dimension_t<E1..., E2...>>> {};
 
   template<Dimension D1, Dimension D2>
-  using dimension_multiply_t = typename dimension_multiply<D1, D2>::type;
+  using dimension_multiply_t = typename dimension_multiply<typename D1::type, typename D2::type>::type;
 
   // dimension_divide
 
@@ -162,6 +181,6 @@ namespace units {
   };
 
   template<Dimension D1, Dimension D2>
-  using dimension_divide_t = typename dimension_divide<D1, D2>::type;
+  using dimension_divide_t = typename dimension_divide<typename D1::type, typename D2::type>::type;
 
 }  // namespace units
diff --git a/src/include/units/quantity.h b/src/include/units/quantity.h
index 9f7a0448..526af801 100644
--- a/src/include/units/quantity.h
+++ b/src/include/units/quantity.h
@@ -254,14 +254,14 @@ namespace units {
     return ret(lhs.count() * rhs.count());
   }
 
-  template<Number Rep1, Exponent... E, Unit U, Number Rep2>
-  quantity<dimension<exp_invert_t<E>...>, unit<dimension<exp_invert_t<E>...>, std::ratio<U::ratio::den, U::ratio::num>>, std::common_type_t<Rep1, Rep2>>
+  template<Number Rep1, Dimension D, Unit U, Number Rep2>
+  quantity<dim_invert_t<D>, unit<dim_invert_t<D>, std::ratio<U::ratio::den, U::ratio::num>>, std::common_type_t<Rep1, Rep2>>
   constexpr operator/(const Rep1& v,
-                      const quantity<dimension<E...>, U, Rep2>& q)
+                      const quantity<D, U, Rep2>& q)
   {
-    using dim = dimension<exp_invert_t<E>...>;
+    using dim = dim_invert_t<D>;
     using ret = quantity<dim, unit<dim, std::ratio<U::ratio::den, U::ratio::num>>, std::common_type_t<Rep1, Rep2>>;
-    using den = quantity<dimension<E...>, U, std::common_type_t<Rep1, Rep2>>;
+    using den = quantity<D, U, std::common_type_t<Rep1, Rep2>>;
     return ret(v / den(q).count());
   }
 
diff --git a/src/include/units/si/frequency.h b/src/include/units/si/frequency.h
index 0d27b3a1..38276e0a 100644
--- a/src/include/units/si/frequency.h
+++ b/src/include/units/si/frequency.h
@@ -27,7 +27,6 @@
 
 namespace units {
 
-  using dimension_frequency = make_dimension_t<exp<base_dim_time, -1>>;
 
   using millihertz = unit<dimension_frequency, std::milli>;
   using hertz = unit<dimension_frequency, std::ratio<1>>;
@@ -35,6 +34,8 @@ namespace units {
   using megahertz = unit<dimension_frequency, std::mega>;
   using gigahertz = unit<dimension_frequency, std::giga>;
   using terahertz = unit<dimension_frequency, std::tera>;
+  struct dimension_frequency : make_dimension_t<exp<base_dim_time, -1>> {};
+  template<> struct dimension_traits<typename dimension_frequency::type> : std::type_identity<dimension_frequency> {};
 
   template<Unit U = hertz, Number Rep = std::intmax_t>
   using frequency = quantity<dimension_frequency, U, Rep>;
diff --git a/src/include/units/si/length.h b/src/include/units/si/length.h
index de31b55c..e7bd8de2 100644
--- a/src/include/units/si/length.h
+++ b/src/include/units/si/length.h
@@ -27,7 +27,8 @@
 
 namespace units {
 
-  using dimension_length = make_dimension_t<exp<base_dim_length, 1>>;
+  struct dimension_length : make_dimension_t<exp<base_dim_length, 1>> {};
+  template<> struct dimension_traits<typename dimension_length::type> : std::type_identity<dimension_length> {};
 
   using millimeter = unit<dimension_length, std::milli>;
   using centimeter = unit<dimension_length, std::ratio<1, 100>>;
diff --git a/src/include/units/si/time.h b/src/include/units/si/time.h
index 41ec3353..e48ed372 100644
--- a/src/include/units/si/time.h
+++ b/src/include/units/si/time.h
@@ -27,14 +27,15 @@
 
 namespace units {
 
-  using dimension_time = make_dimension_t<exp<base_dim_time, 1>>;
-
   using nanosecond = unit<dimension_time, std::nano>;
   using microsecond = unit<dimension_time, std::micro>;
   using millisecond = unit<dimension_time, std::milli>;
   using second = unit<dimension_time, std::ratio<1>>;
   using minute = unit<dimension_time, std::ratio<60>>;
   using hour = unit<dimension_time, std::ratio<3600>>;
+  struct dimension_time : make_dimension_t<exp<base_dim_time, 1>> {};
+  template<> struct dimension_traits<typename dimension_time::type> : std::type_identity<dimension_time> {};
+
 
   template<Unit U = second, Number Rep = std::intmax_t>
   using time = quantity<dimension_time, U, Rep>;
diff --git a/src/include/units/si/velocity.h b/src/include/units/si/velocity.h
index adb6ca67..d8c85172 100644
--- a/src/include/units/si/velocity.h
+++ b/src/include/units/si/velocity.h
@@ -28,7 +28,8 @@
 
 namespace units {
 
-  using dimension_velocity = make_dimension_t<exp<base_dim_length, 1>, exp<base_dim_time, -1>>;
+  struct dimension_velocity : make_dimension_t<exp<base_dim_length, 1>, exp<base_dim_time, -1>> {};
+  template<> struct dimension_traits<typename dimension_velocity::type> : std::type_identity<dimension_velocity> {};
 
   using meter_per_second = unit<dimension_velocity, std::ratio<1>>;
   using kilometer_per_hour = unit<dimension_velocity, std::ratio<1000, 3600>>;