Hey test preppers!

I'm extremely excited to announce that I'm collaborating with Gohar's Guide and Mahad the Mentor to bring you all a brand new SAT Bootcamp! This bootcamp will be a comprehensive program geared at prepping you for the August SAT, complete with tons of live, interactive lessons led by yours truly.

We’ve had a lot of new students join the waitlist recently, so if you'd like to secure your spot and stay in the know, be sure to join here.

But anyways, how did this partnership come about?

My name is Dan Bouzolin, and I actually went to the same high school as Mahad and Gohar. We all scored in the top 1% on our SAT/ACTs, but Mahad and Gohar founded Next Admit, whereas I started Dan’s Test Prep. So as the tutor, I’ll be dishing out some fresh SAT tips each week leading up to the bootcamp.

This week’s tip focuses on exponents and radicals, a topic that you’ll see pop up largely as part of the Advanced Math domain. I’m going to assume you have some basic working knowledge, but here’s the rundown: exponents are basically repeated multiplication (in the same way that multiplication is repeated addition), and radicals “undo” exponents (much like division undoes multiplication). From those simple facts, you can probably see how radicals and exponents go hand in hand.

Let’s take a look at an example problem.

This problem asks us to find the value of a/b, and given the nature of the problem, we’ll need to use a few exponent and radical rules. The first rule I’ll use is one of the more important ones: converting radicals to fractional exponents. To do this, all you need to know is that the exponent becomes the numerator and the root becomes the denominator.

Knowing this, you can simplify the original equation into the following:

The next rule you’ll need to apply is the division of two like bases, where we simply subtract the exponents from each other. This further simplifies the left hand side as follows:

This is about as simplified as we’re going to get it. I’ve kept the left hand side as a fraction because as you can see, the right hand side is also a fraction (important clue). Since we have the same base, we can equate the two exponents and conclude that a/b = 7/6.

Of course, you can always use Desmos for a problem like this, but you might be stuck trying to guess the values of a and b for longer than it actually takes to solve by hand. (How to properly use Desmos is one of the topics we’ll cover more in-depth during the bootcamp, by the way).

I tried using Desmos and… yeah. It’s great, but definitely better for some problems than others.

Anyways, hope you learned something new, and as a thanks for reading, I’m sending you all my Exponents and Radicals Cheat Sheets!

See you next week.

~ Dan

P.S. If you've already joined, you can move up the waitlist by sharing this email using the link below 🤭