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1. Find unit digit of product (173)⁴⁵ × (152)⁷⁷ × (777)⁹⁹⁹.

A. 4

B. 2

C. 8

D. 6

Solution:

To find unit digit of a number or an Expression, We have to divide the number or expression by 10 and the remainder obtained by this operation would be the required unit digit.

\begin{aligned} \frac{{(173)}^{45} \times {(152)}^{77} \times {(777)}^{999}}{10} \\ Remainder would be same as, \\ \frac{3^{45} \times 2^{77} \times 7^{999}}{10} \\ O r, \frac{3 \times 2 \times 7^{3}}{10} \\ O r, \frac{6 \times 343}{10} \\ Remainder would be same as \frac{6 \times 3}{10} \end{aligned}

Thus, Required remainder and unit digit will be 8.

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