Soon I’ll be teaching rational exponents in algebra 2. I’ve never found an intuitive way of teaching it…until now. Thanks Bowen.

The approach leverages geometric sequences. I’d love to regurgitate it, but this tweet from Bowen is my source and sums it up:

.@mpershan @TypeAMathLand @davidwees Yeah, I might have helped a bit there :)

27 x 2/3 is to 27^{2/3} as addition is to multiplication pic.twitter.com/cvnNPjUsP5

— Bowen Kerins 🔗 (@bowenkerins) October 30, 2016

The unit prior focused on sequences with a heavy emphasis on geometric sequences, so this is the perfect bridge to developing this idea that most students find confusing. It all comes back to repeated multiplication, as it should.

In the past, I’ve usually had students enter various expressions (e.g. 100^(1/2)) into their calculators to stumble upon the relationship between rational exponents and radicals:

But this painfully ignores the mathematics behind exponentiation and instead lures them into believing that these two concepts are magically connected through a few keystrokes on their calculator. It treats rational exponents as an isolated concept and unrelated to repeated multiplication.

After discovering my new strategy for teaching rational exponents, I found this video from Vi Hart on logarithms. The similarities run deep.

Now I can’t wait to teach logarithms.

bp