## 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, *x*^{5} 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) ; *for example*, .

2. (2) ; *for example*, .

3. (3) ; *for example*, .

4. (4) ; *for example*, .

5. (5) ; *for example*, .

6. (6) ; *for example*, .

7. (7) ; for example, .

8. (8) ; *for example*, *and* .

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.