How to Add & Multiply Exponents

By Ruby Martes; Updated April 24, 2017

Exponents show how many times a number is multiplied by itself. For example, 2^3 (pronounced "two to the third power," "two to the third" or "two cubed") means 2 multiplied by itself 3 times. The number 2 is the base and 3 is the exponent. Another way of writing 2^3 is 2_2_2. The rules for adding and multiplying terms containing exponents are not difficult, but they may seem counter-intuitive at first. Study examples and do some practice problems, and you will soon get the hang of it.

Adding exponents

Check the terms that you want to add to see if they have the same bases and exponents. For example, in the expression 3^2 + 3^2, the two terms both have a base of 3 and an exponent of 2. In the expression 3^4 + 3^5, the terms have the same base but different exponents. In the expression 2^3 + 4^3, the terms have different bases but the same exponents.

Add terms together only when the bases and exponents are both the same. For example, you can add y^2 + y^2, because they both have a base of y and an exponent of 2. The answer is 2y^2, because you are taking the term y^2 two times.

Compute each term separately when either the bases, the exponents or both are different. For example, to compute 3^2 + 4^3, first figure out that 3^2 equals 9. Then figure out that 4^3 equals 64. After you have computed each term separately, then you can add them together: 9 + 64 = 73.

Multiplying exponents

Check to see if the terms you want to multiply have the same base. You can only multiply terms with exponents when the bases are the same.

Multiply the terms by adding the exponents. For example, 2^3 * 2^4 = 2^(3+4) = 2^7. The general rule is x^a * x^b = x^(a+b).

Compute each term separately if the bases in the terms are not the same. For example, to calculate 2^2 * 3^2, you have to first calculate that 2^2 = 4 and that 3^2 = 9. Only then can you multiply the numbers together, to get 4 * 9 = 36.

About the Author

Ruby Martes has been writing professionally since 1985, specializing in pop culture, quitting smoking and odd bits of trivia. Martes has a Bachelor of Arts in psychology from the University of California, Berkeley, a Master of Arts in English/creative writing from San Francisco State and a Juris Doctor from University of California, Hastings, where she was a law journal editor.