What is the sum of the units digits of 536^44 and 334^89?

6 to the power of any integer will ALWAYS have a 6 as a units digit
4 to the power of any number will ALWAYS render a 6 or a 4. Odd powers give a "4" units digit, even powers give a "6" units digit

4+6=10

Simple pattern recognition

Multiplication of the numbers will not even interfere with the units digit and you can quickly spot that simply multiplying the units digit will provide you with the pattern, so:

6*6= 6*6 = 6 so the pattern of 536^44 is that the UD is always 6.

On to 334. This one is a true pattern and not just a repetition. Looking ONLY at the units digit:

4*4 = 6
6*4 = 4
4*6 = 6

You can see that every odd power will yield a 4 and every even power will yield a 6. Therefore, your answer for this second exponential term is 4.

6+4 = 10

Just a word of caution: Be wary of alternating patterns when counting even and odd exponents. Be sure to count the FIRST TERM as ONE and not skip over it entirely to assign the product term as the result of the first power. Simple mistakes often lead to frustration (and I've had plenty of that lately).

Cyclicity of 6 is 1, so 536^44 will have units digit as 6

Cyclicity of 4 is 2 , so 334^88 will have units digit as 6 ; for the additional 334 units digit will be 4

So, the sum of unit digits will be : 6+4 = 10

What is the sum of the units digits of 536^44 and 334^89?

A. 2
B. 4
C. 8
D. 10
E. 12

Unit digit for 536^44 is 6
Unit digit for 334^89 is 4
Sum is 6+4 = 10
Answer: D