Question:Find the unit's digit in the product `( 3^67 xx 6^39 xx 7^53 )`
Answer Clearly, unit digit in `3^4` is 1. ∴ Unit digit in `3^64` is 1. ∴ Unit digit in `3^67` is 7. [Because Unit digit in `1 xx 3 xx 3 xx 3` is `7` ] Clearly, unit digit in every power of 6 is 6 ∴ Unit digit in `6^39` is 6. Clearly, unit digit in `7^4` is 1. ∴ Unit digit in `7^52` is 1. ∴ Unit digit in `7^53` is 7. [Because Unit digit in `1 xx 7` is 7 ] ∴ Unit digit in given product = Unit digit in `( 7 xx 6 xx 7 ) = 4`.
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Find the unit's digit in the product `( 3^67 xx 6^39 xx 7^53 )`