Exponents are a shorthand method of describing how many times a particular number is being multiplied by itself. To write in exponent form, we would simply count out how many 3s were being multiplied together (in this case five), and then write 3⁵. In written or verbal form, 3⁵ is stated as: “three to the fifth power.”

There are a number of exponent terms that are important to know. The SAT will not directly test you on this knowledge, but you should know these terms if you are going to discuss or learn about exponents.

When you take the SAT, you should already know the squares of numbers 1 through about 15. Memorizing this little chart can save you a lot of time on the test.

You should also know that 2 cubed (2³) = 8 and that 3³ = 27, and—just to be safe—that 4³ = 64 and 5³ = 125.

Actually, you can’t add or subtract numbers with exponents. Instead, you have to work out each exponent to find its value and then add the two numbers. For example, to add 3³ + 4², you must work out the exponents to get and then calculate 27 + 16 = 43. (You probably don’t need to write out the whole first step when doing a problem like this one. We included it just to be complete.) Often, you can work out exponents on your calculator, so figure out how to use your calculator’s exponent functions before the test. It can save you time and increase your accuracy.

To multiply two base exponential numbers that have the same base, all you have to do is add the exponents together:

To divide two same-base exponential numbers, just subtract the exponents.

If you need to multiply or divide two exponential numbers that do not have the same base or exponent, you’ll just have to do your work the old-fashioned way: multiply the exponential numbers out and multiply or divide them accordingly.

Occasionally you might see an exponent raised to another exponent, as seen in the following format (3²)⁴. In such cases, multiply the exponents:

To raise a fraction to an exponent, raise both the numerator and denominator to that exponent:

When you multiply a negative number by a negative number, you get a positive number, and when you multiply a negative number by a positive number, you get a negative number. These rules affect how negative numbers function in reference to exponents.

The square root of a number is the number that, when squared (multiplied by itself), is equal to the given number. For example, the square root of 16 is 4, because A perfect square is a number whose square root is an integer.

The sign denoting a square root is . To use the previous example, As with exponents, you need to know how to multiply and divide square roots.

As the example shows, to multiply two square roots, you should multiply the numbers within each individual square root and place the product under a single square root.

This rule also works in reverse, so you can take a number within a and factor it into perfect squares.

Notice in this example that once we separated out 16 from 48, we could change the into 4. This skill is important for the SAT. When dealing with square roots, you may get an answer that looks quite different from any of the answer choices. In such situations, you probably have just neglected to reduce the number within the square-root sign.

Just as when you multiply square roots, when you divide them, you can divide the numbers and place them under a single square root.

To find the square root of a fraction, take the square root of both the numerator and the denominator. For example, = ¹/₄. In some instances, either the numerator or denominator might not be a perfect square. In these instances, you won’t be able to get rid of the sign. For example, = .