diff --git a/src/DirectProducts.jl b/src/DirectProducts.jl
index e390ccf..2d30fcb 100644
--- a/src/DirectProducts.jl
+++ b/src/DirectProducts.jl
@@ -271,7 +271,7 @@ end
 > Return the direct-product group operation of elements, i.e. component-wise
 > operation as defined by `operations` field of the parent object.
 """
-function *(g::DirectProductGroupElem{T}, h::DirectProductGroupElem{T}, check::Bool=true) where {T}
+function *(g::DirectProductGroupElem, h::DirectProductGroupElem, check::Bool=true)
    if check
       parent(g) == parent(h) || throw(DomainError(
          "Can not multiply elements of different groups!"))
@@ -279,6 +279,8 @@ function *(g::DirectProductGroupElem{T}, h::DirectProductGroupElem{T}, check::Bo
    return DirectProductGroupElem([a*b for (a,b) in zip(g.elts,h.elts)])
 end
 
+^(g::DirectProductGroupElem, n::Integer) = Base.power_by_squaring(g, n)
+
 @doc doc"""
     inv(g::DirectProductGroupElem)
 > Return the inverse of the given element in the direct product group.
diff --git a/src/WreathProducts.jl b/src/WreathProducts.jl
index ec985cd..a383b32 100644
--- a/src/WreathProducts.jl
+++ b/src/WreathProducts.jl
@@ -182,6 +182,8 @@ function *(g::WreathProductElem, h::WreathProductElem)
    return WreathProductElem(g.n*g.p(h.n), g.p*h.p, false)
 end
 
+^(g::WreathProductElem, n::Integer) = Base.power_by_squaring(g, n)
+
 @doc doc"""
     inv(g::WreathProductElem)
 > Returns the inverse of element of a wreath product, according to the formula