An exponent defines the number of times a number is to be multiplied by itself. For example, in ab, where a is the base, and b the exponent, a is multiplied by itself b times. In a numerical example, 25 = 2 
2 
2 
2 
2. An exponent can also be referred to as a power: a number with an exponent of 2 is raised to the second power. There are some other terms that you should be familiar with:
- Base. The base refers to the 3 in 35. It is the number that is being multiplied by itself however many times specified by the exponent.
- Exponent. The exponent (or power) is the 5 in 35. The exponent tells how many times the base is to be multiplied by itself.
- Square. Saying that a number is “squared” means that it has been raised to the second power, i.e., that it has an exponent of 2. In the expression 62, 6 has been squared.
- Cube. Saying that a number is “cubed” means that it has been raised to the third power, i.e., that it has an exponent of 3. In the expression 43, 4 has been cubed.
Common Exponents
It may be worth your while to memorize a few common exponents before the test. Knowing these regularly used exponents can save you the time it would take to calculate them during the test. Here is a list of squares from 1 through 10:
Memorizing the first few cubes can be helpful as well:
Finally, the first few powers of two are useful for many applications:
Adding and Subtracting Numbers with Exponents
In order to add or subtract numbers with exponents, you have to first find the value of each power, and then add the two numbers. For example, to add 3
3 + 4
2, you must expand the exponents to get (3
3
3) + (4
4), and then, finally, 27 + 16 = 43.
If you’re dealing with algebraic expressions that have the same bases and exponents, such as 3x4 and 5x4, then they can simply be added and subtracted. For example, 3x4 + 5x4 = 8x4.
Multiplying and Dividing Numbers with Exponents
To multiply exponential numbers or terms that have the same base, add the exponents together:
To divide two same-base exponential numbers or terms, just subtract the exponents.
To multiply exponential numbers raised to the same exponent, raise their product to that exponent:
To divide exponential numbers raised to the same exponent, raise their quotient to that exponent:
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 the result accordingly.
Raising an Exponent to an Exponent
Occasionally you might encounter an exponent raised to another exponent, as seen in the following formats (32)4 and (x4)3. In such cases, multiply the powers:
