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Lucas Fink

Basic Exponents Rules on the SAT

Let’s rewind to well before you started thinking about the SAT. Do you remember learning addition and subtraction? Alright, so it was a long time ago, and most of us don’t have very clear memories from first grade, other than that time Amy Carson ate a dead fly off the radiator and you got in trouble for it. But you probably remember being posed with a question along the lines of “If I have 30 gummy bears, and you eat the arms off 17 of them, how many gummy bears that can do pushups do I have left?” An unimaginative kid might’ve said zero, believing gummy bears don’t buff up, but the rest of us learned how to “take away” using concrete images like that..

We could picture the situation that the equation described. Moving up to multiplication, it was still relatively quick to find real world applications. By the time we got to exponents, though, things started getting kind of abstract, especially when dealing with roots.

So knowing how to deal with exponents on your SAT might get you a little confused at points if you can’t remember a few rules that aren’t so easy to figure out by yourself. You’ll need to remember them, even if you don’t quite understand why they are true.


Radicals other than square roots

Numbers over radicals occasionally throw people off. Just remember that it’s the opposite process of exponents. So if 2^3 is 2*2*2=8, then root{3}{8}=2. This is totally fundamental, but it’s a good place to start.

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Fractions in exponents

These are just the same as above. If you see a fraction in an exponent on your SAT, go right ahead and convert it into a radical. So 8^{1/3} equals 2, just the same as root{3}{8}=2.

If you have something other than a 1 in the numerator, like 8^{2/3}, then just put the denominator into the radical and keep the numerator as an exponent: root{3}{8}^2. From there, it doesn’t matter which operation you carry out first. 2^2=4 just as root{3}{64}=4.


0 in an exponent

Any number to the 0th power is one. 2^0=1 and 9,999^0=1. We don’t need to worry about why for the purposes of the SAT (but if you enjoy math puzzles and want to figure it out, here’s a hint: it has to do with the next fact).


Negatives in exponents

Careful not to get x^-2 confused with x^{1/2}. Instead, x^-2=1/x^2. Although fractions in exponents are tested more often, negatives are also liable to show up on your SAT, so you should get comfortable with this if you aren’t already.

How you can imagine that using gummy bears, I’m not sure, but that doesn’t make it difficult to use—and that’s true for all of the rules above. As long as you know the facts, you can work pretty easily with exponents on your SAT that might seem daunting at first.


About Lucas Fink

Lucas is the teacher behind Magoosh TOEFL. He’s been teaching TOEFL preparation and more general English since 2009, and the SAT since 2008. Between his time at Bard College and teaching abroad, he has studied Japanese, Czech, and Korean. None of them come in handy, nowadays.

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