diff --git a/pkg/sql/plan/function/func_binary.go b/pkg/sql/plan/function/func_binary.go
index 960a6aa488789..5a44ef429c19f 100644
--- a/pkg/sql/plan/function/func_binary.go
+++ b/pkg/sql/plan/function/func_binary.go
@@ -6722,6 +6722,13 @@ func Power(ivecs []*vector.Vector, result vector.FunctionResultWrapper, _ *proce
 	rs := vector.MustFunctionResult[float64](result)
 
 	for i := uint64(0); i < uint64(length); i++ {
+		if selectList != nil && (selectList.IgnoreAllRow() ||
+			(!selectList.ShouldEvalAllRow() && selectList.Contains(i))) {
+			if err = rs.Append(0, true); err != nil {
+				return err
+			}
+			continue
+		}
 		v1, null1 := p1.GetValue(i)
 		v2, null2 := p2.GetValue(i)
 		if null1 || null2 {
@@ -6729,8 +6736,11 @@ func Power(ivecs []*vector.Vector, result vector.FunctionResultWrapper, _ *proce
 				return err
 			}
 		} else {
-			//TODO: Ignoring 4 switch cases:https://github.com/m-schen/matrixone/blob/0c480ca11b6302de26789f916a3e2faca7f79d47/pkg/sql/plan/function/builtin/binary/power.go#L36
 			res := math.Pow(v1, v2)
+			if math.IsNaN(res) || math.IsInf(res, 0) {
+				return moerr.NewOutOfRangeNoCtxf(
+					"float64", "DOUBLE value is out of range in 'pow(%v,%v)'", v1, v2)
+			}
 			if err = rs.Append(res, false); err != nil {
 				return err
 			}
diff --git a/pkg/sql/plan/function/func_binary_test.go b/pkg/sql/plan/function/func_binary_test.go
index 1b14388493131..4f3d19ac11aed 100644
--- a/pkg/sql/plan/function/func_binary_test.go
+++ b/pkg/sql/plan/function/func_binary_test.go
@@ -5033,6 +5033,68 @@ func TestPower(t *testing.T) {
 	}
 }
 
+func TestPowerOutOfRange(t *testing.T) {
+	testCases := []struct {
+		name      string
+		bases     []float64
+		exponents []float64
+	}{
+		{name: "negative base with fractional exponent", bases: []float64{-2}, exponents: []float64{0.5}},
+		{name: "zero base with negative exponent", bases: []float64{0}, exponents: []float64{-1}},
+		{name: "invalid value after valid value", bases: []float64{2, -2}, exponents: []float64{3, 0.5}},
+	}
+
+	proc := testutil.NewProcess(t)
+	for _, tc := range testCases {
+		t.Run(tc.name, func(t *testing.T) {
+			tcc := NewFunctionTestCase(
+				proc,
+				[]FunctionTestInput{
+					NewFunctionTestInput(types.T_float64.ToType(), tc.bases, nil),
+					NewFunctionTestInput(types.T_float64.ToType(), tc.exponents, nil),
+				},
+				NewFunctionTestResult(types.T_float64.ToType(), true, []float64{0}, nil),
+				Power,
+			)
+
+			require.NoError(t, tcc.result.PreExtendAndReset(tcc.fnLength))
+			_, err := tcc.DebugRun()
+			require.Error(t, err)
+			require.True(t, moerr.IsMoErrCode(err, moerr.ErrOutOfRange))
+			require.ErrorContains(t, err, "DOUBLE value is out of range")
+		})
+	}
+}
+
+func TestPowerRespectsSelectList(t *testing.T) {
+	proc := testutil.NewProcess(t)
+	inputs := []FunctionTestInput{
+		NewFunctionTestInput(types.T_float64.ToType(), []float64{-2, 2}, nil),
+		NewFunctionTestInput(types.T_float64.ToType(), []float64{0.5, 3}, nil),
+	}
+	tcc := NewFunctionTestCase(
+		proc,
+		inputs,
+		NewFunctionTestResult(types.T_float64.ToType(), false, []float64{0, 8}, []bool{true, false}),
+		Power,
+	)
+	require.NoError(t, tcc.result.PreExtendAndReset(tcc.fnLength))
+
+	selectList := &FunctionSelectList{
+		AnyNull:    true,
+		SelectList: []bool{false, true},
+	}
+	err := Power(tcc.parameters, tcc.result, proc, tcc.fnLength, selectList)
+	require.NoError(t, err)
+
+	resultVec := tcc.result.GetResultVector()
+	require.True(t, resultVec.GetNulls().Contains(0))
+	resultParam := vector.GenerateFunctionFixedTypeParameter[float64](resultVec)
+	value, isNull := resultParam.GetValue(1)
+	require.False(t, isNull)
+	require.Equal(t, float64(8), value)
+}
+
 // TRUNCATE
 func initTruncateTestCase() []tcTemp {
 	cases := []struct {
diff --git a/test/distributed/cases/function/func_math_power.result b/test/distributed/cases/function/func_math_power.result
index a2d53f162a3fd..d2d5446617829 100644
--- a/test/distributed/cases/function/func_math_power.result
+++ b/test/distributed/cases/function/func_math_power.result
@@ -19,6 +19,16 @@ result5
 SELECT POWER(4, 0.5) AS result6;
 result6
 2.0
+SELECT POW(-2, 0.5);
+Data truncation: data out of range: data type float64, DOUBLE value is out of range in 'pow(-2,0.5)'
+SELECT POWER(0, -1);
+Data truncation: data out of range: data type float64, DOUBLE value is out of range in 'pow(0,-1)'
+SELECT IF(0, POW(-2, 0.5), 1);
+IF(0, POW(-2, 0.5), 1)
+1.0
+SELECT CASE WHEN 0 THEN POWER(0, -1) ELSE 1 END;
+case when 0 then POWER(0, -1) else 1 end
+1.0
 SELECT POW(2, 3) = POWER(2, 3) AS same_result;
 same_result
 1
diff --git a/test/distributed/cases/function/func_math_power.test b/test/distributed/cases/function/func_math_power.test
index 24b51a69d6776..95859c5a57ea4 100644
--- a/test/distributed/cases/function/func_math_power.test
+++ b/test/distributed/cases/function/func_math_power.test
@@ -9,6 +9,12 @@ SELECT POWER(2, 3) AS result4;
 SELECT POWER(2, 0) AS result5;
 SELECT POWER(4, 0.5) AS result6;
 
+#SELECT - Out-of-range results
+SELECT POW(-2, 0.5);
+SELECT POWER(0, -1);
+SELECT IF(0, POW(-2, 0.5), 1);
+SELECT CASE WHEN 0 THEN POWER(0, -1) ELSE 1 END;
+
 #SELECT - Verify POW and POWER are aliases
 SELECT POW(2, 3) = POWER(2, 3) AS same_result;
 
@@ -75,4 +81,3 @@ create table t1(a float,  b float);
 insert into t1 values(14.3, 4.413), (9.123, 9.409);
 select b from t1 group by b having power(1,b)>0;
 drop table t1;
-