### 1.2 – Exponents and Radicals

## Video 1 of 4: Zero and Negative Exponents

## Video 2 of 4: Laws of Exponents

## Video 3 of 4: Scientific Notation

## Video 4 of 4: Radicals and Root Properties

# Exponents and Radicals

### Exponential Notation

Exponential notation is the mathematical way of writing a repeated multiplication. For example, can be written in exponential notation as indicating that there are four factors of 3. In general, exponential notation is defined as follows:

The number is called the **base**. The number is called the **exponent.**

### Zero and Negative Exponents

An exponent need not be a positive number. In fact, exponents can also be zero, or negative. We define these cases by:

If is any real number, and is any positive integer, then

### Laws of Exponents

The nature of exponents lends to the following rules, or laws, of exponents.

### Scientific Notation

Exponents are used in the expression of very large or very small numbers. For example, the number 125,000,000,000 can be written

Where and is an integer

### Definition of n-th Root

For any positive integer , the **principal** **root** of is: which is equivalent with

### Properties of n-th Roots

if is odd

if is even

### Definition of Rational Exponents

For any rational exponent in lowest terms, where are integers, and ,

or equivalently