Find the remainder when 5^23 + 4^6 is divided by 10

Question

How would I go about solving this using modular arithmetic?

Answer 1

Hint:

$5^k \equiv 5\pmod {10}$

$4^{2k+1} \equiv 4\pmod {10}$

$4^{2k} \equiv 6\pmod {10}$