What is the unit digit of the product 3^65 * 6^59*7^71

1.	What is the unit digit of the product 3^65 * 6^59*7^71
Answer» 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:

Answer»

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

3^65 * 6^59 * 7^71

= 3^1 * 6 * 7^3

= 3 * 6 * 3

= 4 <--- last/unit digit.

Step-by-step explanation:

Discussion