The exponent the a number says how countless times to usage the number in a multiplication.

You are watching: -3 to the 4th power In 82 the "2" states to use 8 twice in a multiplication,so 82 = 8 × 8 = 64

In words: 82 can be referred to as "8 come the strength 2" or "8 come the 2nd power", or merely "8 squared"

Exponents are likewise called powers or Indices.

Some more examples:

### Example: 53 = 5 × 5 × 5 = 125

In words: 53 can be referred to as "5 to the 3rd power", "5 to the power 3" or just "5 cubed"

### Example: 24 = 2 × 2 × 2 × 2 = 16

In words: 24 might be referred to as "2 come the fourth 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 of those a"s: ## Another method of writing It

Sometimes human being use the ^ price (above the 6 on her keyboard), as it is simple to type.

## Negative Exponents

Negative? What could be opposing of multiplying? Dividing!

So we divide by the number each time, which is the exact same as multiply by 1number

## Negative? flip the Positive! That last example showed one easier way to handle negative exponents: calculation the optimistic exponent (an)

More Examples:

an adverse Exponent mutual 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, then you just have actually the number chin (example 91 = 9) 0 If the exponent is 0, then you gain 1 (example 90 = 1) But what around 00 ? It can be one of two people 1 or 0, and also so world say it is "indeterminate".

## It All provides Sense

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

Example: strength of 5
.. Etc..

See more: Watch Dance Moms Season 5 Episode 28 Review W/ Kira Girard, Season 5 Episode 28 52 5 × 5 25
51 5 5
50 1 1
5-1 15 0.2
5-2 15 × 15 0.04
.. Etc..