Find the unit digit of 3^66*6^41*7^53
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The answer is 2.010868e95
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3^66
(3^4)^16* 3^2...3^4 will have the unit digit = 1, hence (3^4)^16 has unit digit = 1
(...1)* 9 = 9
Unit digit of 3^66 = 9
6^41
6^n will always have an unit digit of 6.. [6^41= 6*6*6*...41 times ; it can be seen 6 multiplied by 6 any number of times will always give unit digit = 6]
Unit digit of 6^41 = 6
7^53
(7^4)^13* 7...... [7^4 will give unit digit = 1, hence (7^4)^13 gives unit digit=1]
(...1)* 7 = 7
Unit digit of 7^53 = 7
Hence, now we have to find the product of all these unit digits:
9*6*7 = ..8
Hence unit digit of 3^66 * 6^41 * 7^53 = 8
Hope it helps.
(3^4)^16* 3^2...3^4 will have the unit digit = 1, hence (3^4)^16 has unit digit = 1
(...1)* 9 = 9
Unit digit of 3^66 = 9
6^41
6^n will always have an unit digit of 6.. [6^41= 6*6*6*...41 times ; it can be seen 6 multiplied by 6 any number of times will always give unit digit = 6]
Unit digit of 6^41 = 6
7^53
(7^4)^13* 7...... [7^4 will give unit digit = 1, hence (7^4)^13 gives unit digit=1]
(...1)* 7 = 7
Unit digit of 7^53 = 7
Hence, now we have to find the product of all these unit digits:
9*6*7 = ..8
Hence unit digit of 3^66 * 6^41 * 7^53 = 8
Hope it helps.
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