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Minh Nguyen

New SAT Math: Exponents and Exponential Expressions

Exponents on the New SAT will test you on your mastery of the basic rules you probably have already learned in math class. The concepts aren’t hard to understand, but it can seem nearly impossible to recall if you haven’t been exposed to them recently.

New SAT test makers will do their best to try to make you fumble your way through an exponents problem by scaring you with seemingly challenging problems. However, once you have the basics down, there’s not much they can do to trick you or cause a silly mistake.

You might be thinking that you can just plug and chug on problems your calculator, but in many cases, simplifying exponents is a lot faster by hand. Furthermore, some problems are impossible to do with a calculator because of the sheer size of the values you need to calculate.

Lastly, you may bump into exponent problems on the non-calculator section, but never fear! Here’s how to tackle them.

New SAT Math: Exponent Rules

Multiplying Exponents

When you multiply two terms that have a base with the same value, add the exponents together to get to your answer. The base value stays the same.

Dividing Exponents

In contrast, when you divide two terms that have a base with the same value, subtract the exponents to get to your answer. The base value stays the same here as well.

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Raising Exponents to a Power

When raising an exponent to a power, multiply the exponents together.

Raising Products to a Power

When raising products to a power, each factor is raised to that power.

New SAT Math: Special Exponents

Exponents to the Power of 0

Anything raised to the power of 0 gives you a value of 1.

Negative Exponents

When you have negative exponent, all you have to do is take the reciprocal of it and rewrite it with a positive exponent. In other words, flip the exponent onto the other side of the fraction line.

Fractional Exponents

The numerator of the exponent tells you the power of the exponent. The denominator of the exponent tells you the index of the radical.

In other words, it’s a two-step problem. You need to raise the term to a certain power, and then take the root of it.

New SAT Math: Simplifying Exponential Expressions


New SAT math exponents -magoosh

Not these kinds of expressions!


You will encounter questions that ask you to simplify exponential expressions. To make the expressions tougher to solve, they’ll usually be multi-step problems involving special exponents and fractions.

When doing problems that have to deal with exponents, stick to the basics. Keep your order of operations in mind, and be careful not to invent math rules that don’t exist.

With a bit of practice, these problems will be a snap for you to overcome on test day!

For more New SAT Math concepts, check out our posts on quadratic equations and how to answer graph and chart questions.

About Minh Nguyen

Minh's passion for helping students succeed grew during his time as a career counselor at the University of California, Irvine. Now, he's helping students all over the world by spilling SAT/ACT secrets through blog posts on Magoosh. When he's not busy tutoring or writing, he enjoys playing guitar, traveling, and talking about himself in third-person.

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