# Properties of Exponents (Powers)

- Author:
- JLF

## 1. Introduction

**Power**is an expression of this type

that represents the result of multiplying the **base**, *a*, by itself as many times as the **exponent**, *b*, indicates. We read it as "*a* to the power of *b*".
**Example 1:
**
The base is 2 and the exponent is 3.

## 2. Exponents properties

**Power of a product Product of powers (same base) Quotient of powers (same base)**

**Power of a quotient Power of a power**

**Negative exponent**

## 3. Examples

**Example 2:**

****We have the multiplication of powers in the numerator, but we can't resolve it because there are different bases (2 and 3). In the denominator we have a power with a base of 6 (3·2). By writing the power in the denominator as the multiplication of powers of bases 3 and 2, we then have the same bases in the numerator and denominator and can now apply the rules.

**Example 3:**

****The difficulty in this problem is the parameters, or what is the same, the letters. We work with them the same way as we do with numbers (the parameters represent numbers after all).