How To Add & Multiply Exponents

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 222. 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.

Step 1

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.

Step 2

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.

Step 3

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.

Step 1

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.

Step 2

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).

Step 3

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.