Question

what is the units digit in the expansion of 3 power 11

Answer 1

Answer: The unit digit is 7.

Step-by-step explanation: To find the unit digit, we do not need to find the complete expansion. For example-in this case we can write

$3^{11}=3^{4}\times 3^{4}\times 3^{3}.$

We know that

$3^{4}=81 ~\textup{and}~ 3^3=27.$

Therefore, the unit digits in the product are $1,~1,~ \textup{and}~7.$

∴ The unit digit in the product is $1\times 1\times 7=7.$

Thus, the unit digit in the expansion is $7.$