is there any natural number n for which(15)n is even number
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No, 15 to the power n cannot end with 0 for any natural number n. It would not possible to get the zero in the last digit, because the unit's place will always get even multiples of 5 or Odd multiples of 5. ... The odd multiples will never have zero in their end digit as only the even multiples tends to have.
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