Without listing all the factors, can you find how many factors each number has?
a) 2401
b) 168
c) 1764

Simplify.
$\left(x^\frac{1}{a-b}\right)^\frac{1}{a-c} \left(x^\frac{1}{b-c}\right)^\frac{1}{b-a} \left(x^\frac{1}{c-a}\right)^\frac{1}{c-b}$

If $x^\frac{1}{2}+x^{-\frac{1}{2}}=a$, write $x^2+x^{-2}$ in terms of $a$.

Find the solution that is not $x=0$ or $x=1$ for the following:
$$\left(\sqrt[4]{x}\right)^{4x^4}=\left(x^4\right)^{4\sqrt[4]{x}}$$
Give your answer as an exponent.

Solve for $x$.
$4^{\sqrt{x^2-2}+x}-5\cdot2^{x-1+\sqrt{x^2-2}}=6$