diff --git a/src/operators.jl b/src/operators.jl
index 311afb73714..7c0ec273ae4 100644
--- a/src/operators.jl
+++ b/src/operators.jl
@@ -197,24 +197,24 @@ end
 
 function Base.:^(lhs::AbstractVariableRef, rhs::Integer)
     T = value_type(typeof(lhs))
-    if rhs == 2
-        return lhs * lhs
+    if rhs == 0
+        return one(T)
     elseif rhs == 1
-        return convert(GenericQuadExpr{T,variable_ref_type(lhs)}, lhs)
-    elseif rhs == 0
-        return one(GenericQuadExpr{T,variable_ref_type(lhs)})
+        return lhs
+    elseif rhs == 2
+        return lhs * lhs
     else
         return GenericNonlinearExpr(:^, Any[lhs, rhs])
     end
 end
 
 function Base.:^(lhs::GenericAffExpr{T}, rhs::Integer) where {T}
-    if rhs == 2
-        return lhs * lhs
+    if rhs == 0
+        return one(T)
     elseif rhs == 1
-        return convert(GenericQuadExpr{T,variable_ref_type(lhs)}, lhs)
-    elseif rhs == 0
-        return one(GenericQuadExpr{T,variable_ref_type(lhs)})
+        return lhs
+    elseif rhs == 2
+        return lhs * lhs
     else
         return GenericNonlinearExpr(:^, Any[lhs, rhs])
     end
diff --git a/test/test_macros.jl b/test/test_macros.jl
index 993fe62a701..3c58375340b 100644
--- a/test/test_macros.jl
+++ b/test/test_macros.jl
@@ -704,9 +704,6 @@ function test_Nonliteral_exponents_in_constraint()
     @variable(model, x)
     foo() = 2
     con1 = @build_constraint(x^(foo()) + x^(foo() - 1) + x^(foo() - 2) == 0)
-    # TODO(odow): `con2` fails to build due to a bug in MutableArithmetics. To
-    # fix, we need MutableArithmetics in the current scope.
-    MutableArithmetics = JuMP._MA
     con2 = @build_constraint(
         (x - 1)^(foo()) + (x - 1)^2 + (x - 1)^1 + (x - 1)^0 == 0
     )
@@ -715,7 +712,7 @@ function test_Nonliteral_exponents_in_constraint()
     @test con1.func == x^2 + x
     @test con2.func == 2 * x^2 - 3 * x
     @test con3.func == 9 * x^2
-    @test con4.func == convert(QuadExpr, 3 * x)
+    @test con4.func == 3 * x
     return
 end
 
diff --git a/test/test_mutable_arithmetics.jl b/test/test_mutable_arithmetics.jl
index d3bc9a33475..9e7489fec29 100644
--- a/test/test_mutable_arithmetics.jl
+++ b/test/test_mutable_arithmetics.jl
@@ -117,11 +117,9 @@ function test_extension_quadratic(
     VariableRefType = VariableRef,
 )
     model = ModelType()
-    @variable(model, w)
-    @variable(model, x)
-    @variable(model, y)
-    @variable(model, z)
-    JuMP._MA.Test.quadratic_test(w, x, y, z)
+    @variable(model, x[1:4])
+    # Test is excluded because of https://github.com/jump-dev/MutableArithmetics.jl/issues/227
+    JuMP._MA.Test.quadratic_test(x...; exclude = ["quadratic_add_canonical"])
     return
 end
 
diff --git a/test/test_operator.jl b/test/test_operator.jl
index 3903c3818e0..ebda3be21b5 100644
--- a/test/test_operator.jl
+++ b/test/test_operator.jl
@@ -376,7 +376,7 @@ function test_extension_basic_operators_variable(
     @test_expression_with_string x * y - 1 "x*y - 1"
     @test_expression_with_string(x^2, "x²", interrable = false)
     @test_expression_with_string(x^1, "x", interrable = false)
-    @test_expression_with_string(x^0, "1", interrable = false)
+    @test x^0 === one(T)
     @test_expression_with_string(x^3, "x ^ 3", interrable = false)
     @test_expression_with_string x^(T(15) / T(10)) "x ^ 1.5"
     # 2-2 Variable--Variable
@@ -444,8 +444,8 @@ function test_extension_basic_operators_affexpr(
         "7.1 x + 2.5",
         inferrable = false
     )
-    @test_expression_with_string(aff^0, "1", inferrable = false)
-    @test_expression_with_string((7.1 * x + 2.5)^0, "1", inferrable = false)
+    @test aff^0 === one(T)
+    @test (7.1 * x + 2.5)^0 === one(T)
     @test_expression_with_string(aff^3, "(7.1 x + 2.5) ^ 3", inferrable = false)
     @test_expression_with_string(
         (7.1 * x + 2.5)^3,
@@ -619,7 +619,7 @@ function test_complex_pow()
     @variable(model, x)
     y = (1.0 + 2.0im) * x
     @test y^0 == (1.0 + 0im)
-    @test y^1 == 0 * y * y + y
+    @test y^1 == y
     @test y^2 == y * y
     @test isequal_canonical(y^3, GenericNonlinearExpr(:^, Any[y, 3]))
     return