Rational exponents are quite confusing
And for the teachers, very amusing
To watch a student struggle along;
And so I help them with this song.

Firstly, b is a real number;
Also greater than zero, so unencumbered
By the role of numbers imaginary—
Listen a while; this'll seem less airy.

Now b is raised to the m/nth power
Where n looks on life without a glower—
Positive our n shall be;
And that's important, you shall see.

Now let's turn this into a radical!
'Twill make it easier to add it all
Up in your head, so you'll understand;
Now b shall be the radicand.

The number of roots is determined by n—
Whether square, cube, quadruple, etc.; and
"What of m?" you ask. It has a job, too;
m is the power you raise the b to!

Does this seem easier? I do hope so,
For I'm not through, in case you didn't know!
You see, rational exponents are radicals,
And we can't leave these in denominators at all.

So if you should see one as the divisor,
"Move it to the top!" says I, your advisor.
This makes the lot look much prettier.
Say, we're done now! Does your head hurt?

I had a high school math teacher who liked to use songs to teach us concepts, and one assignment she gave us was to create such a song or poem. Here's mine. It gives me Dr. Seuss vibes.