Question

the unit digit of 214 rest to power 24 is
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Answer 1

Answer:

214^24 is 8.51001×10^55

Step-by-step explanation:

so units digit would be 8

Answer 2

Answer:

$unit \: digit \: of \: {214}^{24} is \: 6$

Step-by-step explanation:

$unit \: digit \: of \: {214}^{24}$

$to \: find \: the \: unit \: digit \: . \: we \: have \: to \: find \: unit \: digit \: of \: {4}^{24}$

Now we observing pattern

${4}^{4} = 256$

${4}^{8} = 65536$

${4}^{12} = 16777216$

${4}^{16} = 4294967296$

${4}^{20} = 1099511627776$

......

By observing pattern , we can say that 4^(4n) always end with 6 , where n = 1,2,3,......

Since 24 is in the form of 4n at n=6

$so \: {4}^{24} \: will \: end \: with \: 6$

$\: so \: {214}^{24} \: \: will \: also \: end \: with \: 6$

$so \: the \: unit \: digit \: of \: {214}^{24} = 6$

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