Question

what is the unit digit in 7^78
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Answer 1

Answer:

Possibilities of unit digit of 7^n are 7,9,3,1.

The unit digit of 7^n gets repeated for every 4th power of 7.

Here, remainder obtained when 78 is divided by 4 is 2

7^78=7^4*19+2 ≅ 7^2

then, unit digit of 7^78 is 9

Answer 2

Answer:

The units digit is 9

Step-by-step explanation:

let us first find only the unit's digit of 7, 7², 7³ ...... till we find a pattern

7= 7

7² = 9

7³ = 3

$7^{4}$ = 1

$7^{5}$ = 7

$7^{6}$ = 9

$7^{7}$ = 3

Now we can see the pattern as 7, 9, 3, 1 and repeat.

So now we should divide the exponent and check if its remainder in either 1, 2, 3, 0

if its remainder is 1 the unit digit is 7, and if its remainder is 2 the unit digit is 9, and if its remainder is 3 the unit digit is 3, and if its remainder is 0 the unit digit is 1

78/4 = (76 + 2)/4

        = 19 + 2/4

therefore, the remainder is 2

So the units digit is 9

happy to help