What is the unit digit in the product (3^{65} x 6^{59} x 7^{71}) ?
Explanation:
Unit digit in 3^{4} = 1 Unit digit in (3^{4})^{16} = 1
Unit digit in 3^{65} = Unit digit in [ (3^{4})^{16} x 3 ] = (1 x 3) = 3
Unit digit in 6^{59} = 6
Unit digit in 7^{4} Unit digit in (7^{4})^{17} is 1.
Unit digit in 7^{71} = Unit digit in [(7^{4})^{17} x 7^{3}] = (1 x 3) = 3
Required digit = Unit digit in (3 x 6 x 3) = 4.
What is the unit digit in 7^{105} ?
Explanation:
Unit digit in 7^{105} = Unit digit in [ (7^{4})^{26} x 7 ]
But, unit digit in (7^{4})^{26} = 1
Unit digit in 7^{105} = (1 x 7) = 7
The unit digit in the product (784 x 618 x 917 x 463) is:
Unit digit in the given product = Unit digit in (4 x 8 x 7 x 3) = (672) = 2
The unit digit of the sum 1289 + 2541 + 8215 + 6137 is:
Solution: The required answer is the unit digit of the sum of the unit digits of the numbers in given sum. i.e., The unit digit of (1289 + 2541 + 8215 + 6137) = the unit digit of (9+1+5+7) = the unit digit of (22) = 2 Hence the answer is 2.
The unit digit of the product 1022 x 729 x 889 x 971 is:
a)2
Solution:
The required answer is the unit digit of the product of the unit digits of the numbers in given product.
i.e, The unit digit of (1022 x 729 x 889 x 971)
= the unit digit of (2 x 9 x 9 x 1)
= the unit digit of (162)
= 2
Hence, the answer is 2.







