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# Exponents

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:

emorizing 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 33 + 42, 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.

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