How to Add Exponents

Adding exponents is one of the three basic rules when dealing with the combination of two bases and powers. The general rule for it is as followed: when you want to multiply the powers with the same base, simply add the two exponents together. In other words, if the bases are the same number, to multiply the two together, simply add the two exponents together to gain the right answer. Before that can be done, though, it is important to understand what a base and exponent are.

What are Bases and Exponents?

When dealing with the multiplication of the same number by itself, you can replace it with bases and exponents. For example, if you wanted to write 2x2x2x2x2 for a math problem, you could write it that way or, instead, you could write 2⁵. In other words, the base was 2 and the exponent was 5. It was 2 to the power of 5 which simply means 2x2x2x2x2. Multiply 2 five times to get the final answer. 2⁵ is equal to 32.

How to Add Exponents

When you have a problem such as 2³2⁷ , one of the things that you might want to do is combine it so that you have only one exponent. The reason for doing this is to keep the problem cleaner and to guarantee that when you solve it, you get the correct answer. Because you have the same base (2), this only requires adding the exponents together to get the answer. In other words:

2³2⁷=2¹⁰

This is the only time, though, that you add the exponents. If it is a scenario such as (2×3)³, instead of adding, you simply do 2³3³. And if the problem is (4²)³, you simply multiply the two powers together and the answer would be 4⁶. However, neither of these scenarios warrants any adding of exponents.

In other words, the only time that you add exponents is when the base is the same. If the base is different, you use one of the other two rules that are available and shown above. However, if the base is the same, simply add the two exponents to get a condensed version.