As indicated in the lessons on multiplying and dividing exponents, it is a requirement that the bases be the same before being able to perform an operation.
When adding and subtracting with exponents, there are two scenarios to consider:
- adding and subtracting with the bases are the same, and
- adding and subtracting with different bases.
Adding and Subtracting with the Same Base:
When you have terms with the same base, they cannot be added together unless you find the value of each term first. The reason for this is that an exponential expression is a multiplication problem. Two or more multiplication problems cannot be added by combining the exponents. Here’s an example:
45 + 42
We know that this means (4 x 4 x 4 x 4 x 4) + (4 x 4)
In order to add these, we have to actually get the values of each term first:
45 + 42 = (4 x 4 x 4 x 4 x 4) + (4 x 4) = 1024 + 16 = 1040
Since this type of problem does follow a set rule, there is no formula to add and subtract exponents.
Adding and Subtracting with Different Bases:
When there are terms with different bases, they cannot be added or subtracted until the values are found for each term.
34 + 23 = (3 x 3 x 3 x 3) + (2 x 2 x 2) = 81 + 8 = 89
The only time you can add or subtract terms with exponents, is when the exponent and the base are exactly the same.
For instance: 42 + 42
There are two terms of 42, so we can write this as 2 x (42) or 2(42).
Similarly, 3(53) – 2(53) = 1(53) or 53