Question

What is the units digit of 2 to the 50th power

Answer 1

Notice that

$2^1=2$
$2^2=4$
$2^3=8$
$2^4=16$
$2^5=32$

so that for each power of 2, there is a pattern of period 4. This means that for integers $k\ge0$, each of $2^{4k}$, $2^{4k+1}$, $2^{4k+2}$, and $2^{4k+3}$ have the same units digit.

We can write $50=4(12)+2$, and since $3=4(0)+2$, it follows that $2^{50}$ and $2^3$ share the same units digits. So the units digit of $2^{54}$ is 8.