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

The remainder according to me should me 4. According to laws of indices, (a^b)^c is the same as a^bc. So, if we use the same formula over here, it would be (32)^32*32, which is 32^1024. This means that 32 is multiplied by itself 1024 times. So what if we take one 32 out of it and divide it by 7. So uf we do that the remainder is 4 and as a result, this is the answer.

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