Your store method is correct. You just need to specify the correct path to your axios post request, which means your component method should be like this :

axios.post('/user/store', {

       first_name: this.user.first_name,

       last_name: this.user.last_name,

       email: this.user.email,

       phone_number: this.user.phone_number,

       is_active: this.user.is_active,

       entity: this.user.entity,

       role_id: this.user.role_id

     }).then((res) => {

          // here clear your form and fetch your users list if you want 

     })

       .catch(error => {

          // here catch error messages from laravel validator and show them 

     });

and your store method should return validator messages error :

public function store(Request $request)

{   

    $validator = Validator::make($request->all(), [

             'first_name' => 'required|max:255',

             'last_name' => 'required|max:255',

             'email' => 'required',

             'is_active' => 'required'

    ]);

    if ($validator->fails()) {

        return response()->json(['errors'=>$validator->errors()],422);

    }



    $user = User::create([

      'first_name' => $request('first_name'),

      'last_name' => $request('last_name'),

      'email' => $request('email'),

      'is_active' => $request('is_active'),

      'phone_number' => $request('phone_number'),

      'role_id' => $request('role_id')

    ]);



    return response()->json([

      'user' => $user,

      'message' => 'Success'

    ], 200);

}