What is the remainder when (32^32)^32 is divided by 7 ?

So actually according to me the remainder should be 4. See, first simplify since in whole power, it can be given as 32^1024. So this means that 32 is multiplied 1024 times and then divided by 7. Since in multiplication, we take one 32 and divide by 7. If 32/7, remainder is 4. So the remainer of (32^32)^32 is 4