What is the units' digit of the following expression $(12)^5*(14)^4*(16)^5$?

We are tasked with finding the units digit of the expression:

$(12)^5 \times (14)^4 \times (16)^5$

To find the units digit, we only need to focus on the units digits of the individual terms. Let's break it down step by step:

Step 1: Units digit of $^5$

The units digit of $12$ is the same as the units digit of $2$, because $12$ ends in a 2.

Now, we calculate the units digit of $2^5$. The powers of 2 cycle every 4 terms in their units digits:

• $2^1 = 2$



• $2^2 = 4$



• $2^3 = 8$



• $2^4 = 6$



• $2^5 = 2$

So, the units digit of $12^5$ is 2.

Step 2: Units digit of (14)^4[/m]

The units digit of $14$ is the same as the units digit of $4$, because $14$ ends in a 4.

Now, we calculate the units digit of $4^4$. The powers of 4 cycle every 2 terms in their units digits: