What is the unit digit of the product 3^65 * 6^59*7^71
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Answer:
3^65 * 6^59 * 7^71
Lets see cycle
3^1 = 3 , 7^1 = 7
3^2 = 9, 7^2 = 9
3^3 = 7, 7^3 = 3
3^4 = 1, 7^4 = 1
3^5 = 3, 7^5 = 7
. .
. .
Last digit of 3 & 7 starts to repeat after 4th power in cycle of 4 I.e (3,9,7,1) & (7,9,3,1)
Power / cycle
65/4 = 1 remainder
So 3^65 can be written as 3^1
71/4 = 3 remainder
So 7^71 can be written as 7^3
Now remember
6^n = 6 <--- last digit
So
3^65 * 6^59 * 7^71
= 3^1 * 6 * 7^3
= 3 * 6 * 3
= 4 <--- last/unit digit.
Step-by-step explanation:
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