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Find the exponent of 80 in 200!. |
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Answer» Correct Answer - 49 `80=2^(4)xx5` To find the exponent of 80 in 200!, we find the exponent of 2 and 5. Exponent of 2 is `[(200)/(2)]+[(200)/(2^(2))]+[(200)/(2^(3))]+[(200)/(2^(4))]+[(200)/(2^(5))]+[(200)/(2^(6))]+[(200)/(2^(7))]` `=100+50+25+12+6+3+1` =197 Exponent of 5 of `[(200)/(5)]+[(200)/(5^(2))]+[(200)/(5^(3))]=40+8+1=49` Now, exponent of 16 in 200! is `[197//4]=49`. Hence, exponent of 80 is 49. |
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