Simplify a variety of algebraic expressions using the laws of exponents:

## Example 1

Simplify

It is important to remember that the exponent applies to only what it is written beside. The exponent applies to the , not to the . Written out in full we have:

In short,

## Example 2

Simplify

The exponent 3 is applied to each factor in the bracket:

## Example 3

Simplify

A negative exponent means to divide repeatedly. We ‘take the reciprocal‘. The result here is a positive number.

## Example 4

Simplify

Let’s see what the result is of a negative exponent on the denominator in general:

Simplify

In short,

Applying this new law, we have and .

## Example 5

Simplify

It is helpful to gather like factors as follows:

## Example 6

Simplify

Let’s make another new law.

Simplify

In short,

Apply this new law to example 6 we have