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# How do you find the unit digit of 312 power 6?

Since neither the three hundred, nor the ten can contribute to the units digit in the answer, you look for a pattern in the units digit in the powers of 2n.

20 = 1

21 = 2

22 = 4

23 = 8

24 = 2

and after that , the pattern repeats, 4, 8, 2, 4, 8, 2, ...

So if n (mod 3) = 1 the units digit is 2

if n (mod 3) = 2 the units digit is 4

and if n (mod 3) = 0 the units digit is 8

where n (mod 3) is the remainder when n is divided by 3.

312 is divisible by 3 [3+1+2=6 is divisible by 3] so 312 mod(3) =0 and so the units digit is 8.

Since neither the three hundred, nor the ten can contribute to the units digit in the answer, you look for a pattern in the units digit in the powers of 2n.

20 = 1

21 = 2

22 = 4

23 = 8

24 = 2

and after that , the pattern repeats, 4, 8, 2, 4, 8, 2, ...

So if n (mod 3) = 1 the units digit is 2

if n (mod 3) = 2 the units digit is 4

and if n (mod 3) = 0 the units digit is 8

where n (mod 3) is the remainder when n is divided by 3.

312 is divisible by 3 [3+1+2=6 is divisible by 3] so 312 mod(3) =0 and so the units digit is 8.

Since neither the three hundred, nor the ten can contribute to the units digit in the answer, you look for a pattern in the units digit in the powers of 2n.

20 = 1

21 = 2

22 = 4

23 = 8

24 = 2

and after that , the pattern repeats, 4, 8, 2, 4, 8, 2, ...

So if n (mod 3) = 1 the units digit is 2

if n (mod 3) = 2 the units digit is 4

and if n (mod 3) = 0 the units digit is 8

where n (mod 3) is the remainder when n is divided by 3.

312 is divisible by 3 [3+1+2=6 is divisible by 3] so 312 mod(3) =0 and so the units digit is 8.

Since neither the three hundred, nor the ten can contribute to the units digit in the answer, you look for a pattern in the units digit in the powers of 2n.

20 = 1

21 = 2

22 = 4

23 = 8

24 = 2

and after that , the pattern repeats, 4, 8, 2, 4, 8, 2, ...

So if n (mod 3) = 1 the units digit is 2

if n (mod 3) = 2 the units digit is 4

and if n (mod 3) = 0 the units digit is 8

where n (mod 3) is the remainder when n is divided by 3.

312 is divisible by 3 [3+1+2=6 is divisible by 3] so 312 mod(3) =0 and so the units digit is 8. Study guides

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## A number a power of a variable or a product of the two is a monomial while a polynomial is the of monomials

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Since neither the three hundred, nor the ten can contribute to the units digit in the answer, you look for a pattern in the units digit in the powers of 2n.

20 = 1

21 = 2

22 = 4

23 = 8

24 = 2

and after that , the pattern repeats, 4, 8, 2, 4, 8, 2, ...

So if n (mod 3) = 1 the units digit is 2

if n (mod 3) = 2 the units digit is 4

and if n (mod 3) = 0 the units digit is 8

where n (mod 3) is the remainder when n is divided by 3.

312 is divisible by 3 [3+1+2=6 is divisible by 3] so 312 mod(3) =0 and so the units digit is 8.  Earn +20 pts  