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

Answer: Option C

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.
$$\begin{array}{rl}& \frac{{\left(173\right)}^{45}\times {\left(152\right)}^{77}\times {\left(777\right)}^{999}}{10}\\ & \text{Remainder}\text{would}\text{be}\text{same}\text{as},\\ & \frac{3^{45}\times 2^{77}\times 7^{999}}{10}\\ & Or,\frac{3\times 2\times 7^3}{10}\\ & Or,\frac{6\times 343}{10}\\ & \text{Remainder}\text{would}\text{be}\text{same}\text{as}\frac{6\times 3}{10}\end{array}$$
Thus, Required remainder and unit digit will be 8.