Find the unit digit of the expression. 36^500×55^200×224^160
Answers
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Given : 36^500×55^200×224^160 ( 36⁵⁰⁰ * 55²⁰⁰ * 224¹⁶⁰)
To find : Unit Digit
Solution:
36⁵⁰⁰ * 55²⁰⁰ * 224¹⁶⁰
any number ending with 6 Raised to power with integer ≥ 1 will end with 6
=> 36⁵⁰⁰ - last digit 6
any number ending with 5 Raised to power with integer ≥ 1 will end with 5
=> 55²⁰⁰ - last digit 5
224¹⁶⁰ = (224)²*⁸⁰ = ((224)² )⁸⁰
now square of any number ending with 4 End with digit 6
and then any number ending with 6 Raised to power with integer ≥ 1 will end with 6
=> ((224)² )⁸⁰ end with 6
=> 224¹⁶⁰ - last digit 6
6 * 5 * 6
= 180
Hence last digit = 0
=> unit Digit = 0
another Simple method
36⁵⁰⁰ * 55²⁰⁰ * 224¹⁶⁰
= 36 * 36⁴⁹⁹ * 55 * 55¹⁹⁹ * 224¹⁶⁰
= 2 * 18 * 36⁴⁹⁹ * 5 * 11 * 55¹⁹⁹ * 224¹⁶⁰
= 2 * 5 * 18 * 11 * 36⁴⁹⁹ * 55¹⁹⁹ * 224¹⁶⁰
= 10 * (18 * 11 * 36⁴⁹⁹ * 55¹⁹⁹ * 224¹⁶⁰)
any number multiplied with 10 end with digit 0
so last digit = 0
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