find the unit digit of 19 to the power 2013 + 11 to the power 2013 - 6 to the power 2013
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Expression is 19²⁰¹³ + 11²⁰¹³ - 6²⁰¹³
for finding unit digit , first of all we have to find unit digit of all individual terms like 19²⁰¹³ , 11²⁰¹³ , 6²⁰¹³ .
Unit digit of 19²⁰¹³ : here you have to memorize that unit place of any number repeats after fourth power . Hence, we have to divide 2013 by 4 , we see remainder is 1 hence, unit digit of 19¹ = 9
similarly unit digit of 11²⁰¹³ = unit digit of 11¹ = 1
until digit of 6²⁰¹³ = unit digit of 6¹ = 6
Now, unit digit of 19²⁰¹³ + 11²⁰¹³ - 6²⁰¹³ = unit digit of 19²⁰¹³ + unit digit of 11²⁰¹³ - unit digit of 6²⁰¹³ = 9 + 1 - 6 = 4
Hence, answer is 4
for finding unit digit , first of all we have to find unit digit of all individual terms like 19²⁰¹³ , 11²⁰¹³ , 6²⁰¹³ .
Unit digit of 19²⁰¹³ : here you have to memorize that unit place of any number repeats after fourth power . Hence, we have to divide 2013 by 4 , we see remainder is 1 hence, unit digit of 19¹ = 9
similarly unit digit of 11²⁰¹³ = unit digit of 11¹ = 1
until digit of 6²⁰¹³ = unit digit of 6¹ = 6
Now, unit digit of 19²⁰¹³ + 11²⁰¹³ - 6²⁰¹³ = unit digit of 19²⁰¹³ + unit digit of 11²⁰¹³ - unit digit of 6²⁰¹³ = 9 + 1 - 6 = 4
Hence, answer is 4
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