# Powerful Problem (hint)

A few weeks ago I posted this “powerful” problem:

Solve $\left(x^2-5x+5\right)^{\left(x^2-9x+20\right)}=1$

Now, allow me to give you a major hint. Consider the simpler equation

$a^b=1$

What are the possible values of $a$ and $b$? Here are the possible combinations:

• $a=1$ and $b$ is anything
• $b=0$ and $a$ is any nonzero number

And here’s the tricky one that most people forget:

• $a=-1$ and $b$ is even

You now have enough information to solve the original equation. I think you’ll be delighted with the solution!