how to use fractional exponents

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how to use fractional exponents

by khaldrogo » Mon Mar 01, 2021 10:16 pm
Just wondering what is the probability of encountering a fractional exponent (eg 6 ^ 1/3) in the GMAT? Can someone help me?
Thanks.

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Hello!

On the GMAT, exponential problems appear more frequently as high-difficulty questions than in low or even medium-difficulty questions. So you can say, there is low probability of encountering a fractional exponent type question in the GMAT.

Therefore, it should be fairly low on your priority list of content areas to brush up on. However, if you are scoring (or hoping to score) in or above the mid-600s, you should spend a little time becoming reacquainted with exponential questions. You’ll be pretty well set for Test Day if you remember what fractional exponents are, how to calculate fractional exponents, and the shortcut for solving difficult fractional exponents problems.

Here are some basic rules:
the numerator of a fractional exponent is a normal exponent: i.e., it raises the quantity to a power (as exponents "normally" do).
the denominator of a fractional exponent represents a root.
if the exponent is negative, then that takes a reciprocal of the quantity.
you can perform these three operations in any order you want; the order that's obviously more sensible is to take the root before raising to the power, so you don't have to deal with obscenely huge numbers.

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Re: how to use fractional exponents

by Ian Stewart » Sat Jun 05, 2021 8:11 am
ManhattanElitePrep wrote:
Sun May 02, 2021 11:40 am
you can perform these three operations in any order you want;
This is not true in general. If you start with the number -2, you can square that, then take the square root, but you cannot square root it first, then square the result, because the square root of a negative number is undefined.

Because square roots are essentially fractional exponents (the exponent 1/2 represents a square root), fractional exponents show up very often on the GMAT, for test takers of any level. It is, however, uncommon (though not unheard of) to see other fractional exponents. The most common fractional exponent that is not a square root is the cube root (the exponent 1/3), and that would not be surprising to see on a test, but any other fractional exponents appear only rarely. Still, if you know how ordinary integer exponents work (which is absolutely essential), and if you understand that a fractional exponent represents some kind of root, there isn't really much you're missing, so you can learn all you need to know about fractional exponents for the GMAT very quickly.
If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com