When $5^{35}-6^{21}$ is evaluated, the units (ones) digit is
(A) 1
(B) 9
(C) 2
(D) 5
(E) 6
First, we note that $5^{35}-6^{21}$ is a positive integer, since

$$
5^{35}-6^{21}=\left(5^{5}\right)^{7}-\left(6^{3}\right)^{7}=3125^{7}-216^{7}
$$

and $3125>216$.

Second, we note that any positive integer power of 5 has a units digit of 5 . Since $5 \times 5=25$ and this product has a units digit of 5 , then the units digit of $5^{3}$ is obtained by multiplying 5 by the units digit 5 of 25 . Thus, the units digit of $5^{3}$ is 5 . Similarly, each successive power of 5 has a units digit of 5 .

Similarly, each power of 6 has a units digit of 6 .

Therefore, $5^{35}$ has a units digit of 5 and $6^{21}$ has a units digit of 6 . When a positive integer with units digit 6 is subtracted from a larger positive integer whose units digit is 5 , the difference has a units digit of 9 .

Therefore, $5^{35}-6^{21}$ has a units digit of 9 .

ANSWER: (B)