# Using Exponents in Algebra

You might like to read the page on Exponents first.

## Whole Number Exponents

The exponent "n" in an says
how many times to use a in a multiplication:

### Example: 53 = 5 × 5 × 5 = 125

• The "3" says to use 5 three times in a multiplication
• In words: 53 could be called "5 to the third power", "5 to the power 3" or simply "5 cubed"

## Negative Exponents

A negative exponent a-n is equal to 1/an (1 divided by the positive exponent)

### Example:

5-3 = 1/53 = 1/125 = 0.008

Also ... by changing the signs of the exponents we get:

A positive exponent an is equal to 1/a-n (1 divided by the negative exponent)

So, we can move an expression between the top and bottom (numerator and denominator) of a fraction when we also change the sign of the exponent.

Example: x-1 = 1/x (a simple reciprocal)

Example: 5-3 = 1/53 = 1/125 = 0.008

## Positive and Negative Together

Here is an example with positive and negative exponents:

### Example: 432-59-132

We can put the values with negative exponents at the bottom (remembering to make the exponents positive):

4332259

Let's simplify it!

32 is 9:

439259

The 9s cancel out:

4325

43 is 4 × 4 × 4 = 64, and
25 is 2 × 2 × 2 × 2 × 2 = 32:

6432

Which simplifies to:

2

Done!

455, 456, 1080, 1081, 2058, 2059, 2060, 2061, 3870, 3871