The exponent of a number claims how numerous times to use the number in a multiplication.

You are watching: -2 to the fourth power

In 82 the "2" says to usage 8 twice in a multiplication,so 82 = 8 × 8 = 64

In words: 82 might be dubbed "8 come the strength 2" or "8 come the 2nd power", or just "8 squared"

Exponents are additionally called powers or Indices.

Some much more examples:

### Example: 53 = 5 × 5 × 5 = 125

In words: 53 can be called "5 come the third power", "5 to the power 3" or simply "5 cubed"

### Example: 24 = 2 × 2 × 2 × 2 = 16

In words: 24 might be called "2 to the 4th power" or "2 to the power 4" or merely "2 come the 4th"

So in general:

 an tells you to main point a through itself,so there space n that those a"s:

## Another way of creating It

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

## Negative Exponents

Negative? What can be opposing of multiplying? Dividing!

So we divide by the number every time, which is the same as multiplying by 1number

## Negative? flip the Positive!

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

More Examples:

an unfavorable Exponent reciprocal ofPositive Exponent price
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, climate you just have the number chin (example 91 = 9) 0 If the exponent is 0, climate you obtain 1 (example 90 = 1) But what about 00 ? It can be either 1 or 0, and also so people say that is "indeterminate".

## It All renders Sense

If girlfriend look at that table, girlfriend will see that positive, zero ornegative exponents space really part of the very same (fairly simple) pattern:

Example: strength 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..