GMAT Quantitative Review

3.0 Math Review

3.2 Algebra

7. Exponents

A positive integer exponent of a number or a variable indicates a product, and the positive integer is the number of times that the number or variable is a factor in the product. For example, x5 means (x)(x)(x)(x)(x); that is, x is a factor in the product 5 times.

Some rules about exponents follow.

Let x and y be any positive numbers, and let r and s be any positive integers.

1.  (1) imagefor exampleimage.

2.  (2) imagefor exampleimage.

3.  (3) imagefor exampleimage.

4.  (4) imagefor exampleimage.

5.  (5) imagefor exampleimage.

6.  (6) imagefor exampleimage.

7.  (7) image; for example, image.

8.  (8) imagefor exampleimage and image.

It can be shown that rules 1–6 also apply when r and s are not integers and are not positive, that is, when r and s are any real numbers.