Finding remainder of a product divided by $8$ with modular arithmetic

Question

I was requested to find the remainder of $9^{52}*7^{33}$ when dividing it by $8$, using modular arithmetic. Let that remainder be $r$. I understand the following will apply:

$9^{52}*7^{33} \equiv r \mod{(8)}$

so that all I must find is the congruence of the product in the module $8$. But how can one go about solving this? I don't have any tries worth showing, since I simply ignore what procedure could be followed.

Answer 1

Hint. Since $9$ is $1$ modulo $8$, so is any power. What can you say about odd powers of $7$ using the same kind of reasoning? To find a modulus after multiplying you multiply the two moduli.

Answer 2

Hint:

$9\equiv 1,\qquad 7 \equiv -1\mod 8.$