diff --git a/test/unit_test/static/quantity_spec_test.cpp b/test/unit_test/static/quantity_spec_test.cpp
index 5ed6c059..60ea4c32 100644
--- a/test/unit_test/static/quantity_spec_test.cpp
+++ b/test/unit_test/static/quantity_spec_test.cpp
@@ -280,6 +280,10 @@ static_assert(is_of_type<kind_of<length> / kind_of<time>, kind_of_<derived_quant
 static_assert(is_of_type<kind_of<length / time>, kind_of_<derived_quantity_spec<length_, per<time_>>{}>>);
 
 // power
+static_assert(is_of_type<pow<0>(length), dimensionless_>);
+static_assert(is_of_type<pow<1>(length), length_>);
+static_assert(is_of_type<pow<2, 2>(length), length_>);
+static_assert(is_of_type<pow<2>(dimensionless), dimensionless_>);
 static_assert(is_of_type<pow<2>(length), derived_quantity_spec<mp_units::power<length_, 2>>>);
 static_assert(is_of_type<pow<1, 2>(length), derived_quantity_spec<mp_units::power<length_, 1, 2>>>);
 static_assert(is_of_type<pow<1, 2>(length* length), length_>);
@@ -293,6 +297,10 @@ static_assert(
 static_assert(is_same_v<decltype(pow<2>(length)), decltype(length * length)>);
 static_assert(is_same_v<decltype(pow<2>(length / time)), decltype(length * length / time / time)>);
 
+static_assert(dimensionless * dimensionless == dimensionless);
+static_assert(is_of_type<dimensionless * dimensionless, dimensionless_>);
+
+
 template<auto& t>
 concept invalid_operations = requires {
   requires !requires { t < t; };
diff --git a/test/unit_test/static/unit_test.cpp b/test/unit_test/static/unit_test.cpp
index 5a689a97..9c9df682 100644
--- a/test/unit_test/static/unit_test.cpp
+++ b/test/unit_test/static/unit_test.cpp
@@ -33,6 +33,7 @@ using namespace mp_units;
 using namespace mp_units::detail;
 
 using one_ = struct one;
+using percent_ = struct percent;
 
 // base dimensions
 // clang-format off
@@ -475,6 +476,12 @@ static_assert(is_of_type<metre / metre, one_>);
 static_assert(is_of_type<si::kilo<metre> / metre, derived_unit<si::kilo_<metre>, per<metre_>>>);
 static_assert(metre / metre == one);
 static_assert(hertz * second == one);
+static_assert(one * one == one);
+static_assert(is_of_type<one * one, one_>);
+static_assert(one * percent == percent);
+static_assert(percent * one == percent);
+static_assert(is_of_type<one * percent, percent_>);
+static_assert(is_of_type<percent * one, percent_>);
 
 static_assert(hertz == 1 / second);
 static_assert(newton == kilogram * metre / square(second));
@@ -492,6 +499,12 @@ static_assert(is_same_v<decltype(pow<2>(mag<3600> * second)), decltype((mag<3600
 static_assert(is_same_v<decltype(pow<2>(metre / second)), decltype(metre * metre / second / second)>);
 static_assert(is_same_v<decltype(pow<2>(kilometre / hour)), decltype(kilometre * kilometre / hour / hour)>);
 
+static_assert(is_of_type<pow<0>(metre), one_>);
+static_assert(is_of_type<pow<1>(metre), metre_>);
+static_assert(is_of_type<pow<2, 2>(metre), metre_>);
+static_assert(is_of_type<pow<2>(one), one_>);
+static_assert(is_of_type<pow<2>(percent), derived_unit<power<percent_, 2>>>);
+static_assert(is_of_type<pow<2>(radian), derived_unit<power<radian_, 2>>>);
 static_assert(is_of_type<pow<2>(metre), derived_unit<power<metre_, 2>>>);
 static_assert(is_of_type<pow<1, 2>(metre), derived_unit<power<metre_, 1, 2>>>);
 static_assert(is_of_type<pow<1, 2>(metre* metre), metre_>);