Determine whether the congruence is true or false. 100equiv 20 mod 8

For the following statement, either prove that they are true or provide a counterexample:
Let a, b, c, d, ${\displaystyle m\in Z}$ such that c, ${\displaystyle d\ge 1}$ and m > 1. If ${\displaystyle a\equiv b\left(\text{mod}m\right)}$ and
${\displaystyle c\equiv d\left(\text{mod}m\right)}$, then ${\displaystyle a^c\equiv b^d\left(\text{mod}m\right)}$

Using Fermat's Little Theorem, solve the congruence ${\displaystyle 2\cdot x^{425}+4\cdot x^{108}-3\cdot x^2+x-4\equiv 0mod107}$.
Write your answer as a set of congruence classes modulo 107, such as {1,2,3}.

Prove that if ${\displaystyle a\equiv b\left(\text{mod}n\right)\text{and}c\equiv d\left(\text{mod}n\right)}$, then if ${\displaystyle a-c\equiv b-d\left(\text{mod}n\right)}$

Prove the transitivity of modular congruence. That is, prove that for all integers a,b,c, and n with n > 1, if $a=b(modn)andb=c(modn)thena=c(modn)$.

Find the smallest positive integer k satisfying the stated condition or explain no such k exists:
${\displaystyle 3^k\equiv 1\text{mod}11}$.

In the roof truss shown, AB=8 and ${\displaystyle m\mathrm{\angle }HAF={37}^{\circ }}$.
Find: ${\displaystyle m\mathrm{\angle }ADB}$
Given:
AB=8 and ${\displaystyle m\mathrm{\angle }HAF={37}^{\circ }}$.
The roof truss has line symmetry.

Figure(1)

To determine: The smallest nonnegative integer x that satisfies the given system of congruences.
${\displaystyle x\equiv 3\pm od5}$
${\displaystyle x\equiv 7\pm od8}$