The exponent that a number says how plenty of times to usage the number in a multiplication.

You are watching: -5 to the 4th power

In 82 the "2" states to use 8 double in a multiplication,so 82 = 8 × 8 = 64

In words: 82 could be called "8 come the strength 2" or "8 come the second power", or merely "8 squared"

Exponents are also called powers or Indices.

Some much more examples:

### Example: 53 = 5 × 5 × 5 = 125

In words: 53 might be referred to as "5 come the 3rd power", "5 come the strength 3" or simply "5 cubed"

### Example: 24 = 2 × 2 × 2 × 2 = 16

In words: 24 might be referred to as "2 to the fourth power" or "2 to the strength 4" or just "2 to the 4th"

So in general:

 an tells you to multiply a by itself,so there space n that those a"s:

## Another means of creating It

Sometimes civilization use the ^ prize (above the 6 on your keyboard), together it is easy to type.

## Negative Exponents

Negative? What could be the opposite of multiplying? Dividing!

So we division by the number every time, i beg your pardon is the very same as multiply by 1number

## Negative? upper and lower reversal the Positive!

 That last instance showed one easier way to handle an unfavorable exponents: calculate the confident exponent (an)

More Examples:

an adverse Exponent mutual ofPositive Exponent prize
4-2 = 1 / 42 = 1/16 = 0.0625
10-3 = 1 / 103 = 1/1,000 = 0.001
(-2)-3 = 1 / (-2)3 = 1/(-8) = -0.125

## What if the Exponent is 1, or 0?

 1 If the exponent is 1, then you just have the number itself (example 91 = 9) 0 If the exponent is 0, climate you acquire 1 (example 90 = 1) But what around 00 ? It might be either 1 or 0, and also so human being say it is "indeterminate".

## It All provides Sense

If you look at the table, friend will see that positive, zero ornegative exponents room really part of the same (fairly simple) pattern:

Example: powers of 5
.. Etc..

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52 5 × 5 25
51 5 5
50 1 1
5-1 15 0.2
5-2 15 × 15 0.04
.. Etc..