diff --git a/src/core/include/units/math.h b/src/core/include/units/math.h
index cc86712b..cdae6963 100644
--- a/src/core/include/units/math.h
+++ b/src/core/include/units/math.h
@@ -58,7 +58,7 @@ template<std::intmax_t Num, std::intmax_t Den = 1, Quantity Q>
     return rep(1);
   } else {
     using dim = dimension_pow<typename Q::dimension, Num, Den>;
-    using unit = downcast_unit<dim, pow<ratio{Num, Den}>(Q::unit::mag)>;
+    using unit = downcast_unit<dim, pow<ratio{Num, Den}>(Q::reference.mag) / dim::mag>;
     using std::pow;
     return quantity<dim, unit, rep>(
       static_cast<rep>(pow(q.number(), static_cast<double>(Num) / static_cast<double>(Den))));
@@ -78,7 +78,7 @@ template<Quantity Q>
   requires requires { sqrt(q.number()); } || requires { std::sqrt(q.number()); }
 {
   using dim = dimension_pow<typename Q::dimension, 1, 2>;
-  using unit = downcast_unit<dim, pow<ratio{1, 2}>(Q::unit::mag)>;
+  using unit = downcast_unit<dim, pow<ratio{1, 2}>(Q::reference.mag) / dim::mag>;
   using rep = TYPENAME Q::rep;
   using std::sqrt;
   return quantity<dim, unit, rep>(static_cast<rep>(sqrt(q.number())));
@@ -97,7 +97,7 @@ template<Quantity Q>
   requires requires { cbrt(q.number()); } || requires { std::cbrt(q.number()); }
 {
   using dim = dimension_pow<typename Q::dimension, 1, 3>;
-  using unit = downcast_unit<dim, pow<ratio{1, 3}>(Q::unit::mag)>;
+  using unit = downcast_unit<dim, pow<ratio{1, 3}>(Q::reference.mag) / dim::mag>;
   using rep = TYPENAME Q::rep;
   using std::cbrt;
   return quantity<dim, unit, rep>(static_cast<rep>(cbrt(q.number())));