Remainder of $3^7/8$ I read here that the remainder of $\frac{ab}{c}$ is equal to the remainder of $\frac{a}{c}\frac{b}{c}$ implying that the remainder of $\frac{a^b}{c}$ is equal to the remainder of $[\frac{a}{c}]^b$. However, when I apply this here, I would get remainder of $[\frac{3}{8}]^7=3^7$ (while the correct answer is $3$). What am I doing wrong here? And if this method is not valid, are there other quick and simple methods of finding remainders like this? 

You may use congruences:
$$3^2=9\equiv1\pmod{8}$$
So
$$3^7=(3^2)^3\times 3\equiv 1\times 3\equiv3\pmod{8}$$
Remember that $a\equiv b\pmod{m}$ means that $a$ and $b$ have same remainder when divided by $m$. It's also equivalent to $m|a-b$ (you read it $m$ divides $a-b$).
And with congruences you can write that if $a\equiv b \pmod{m}$ and $c\equiv d \pmod{m}$, then, among others:
$$ac\equiv bd \pmod{m}$$
$$a+c\equiv b+d \pmod{m}$$
