The exponent that a number states how countless times to use the number in a multiplication.

You are watching: 10 to the power of -3

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

In words: 82 might be dubbed "8 come the power 2" or "8 to the second power", or merely "8 squared"

Exponents are additionally called powers or Indices.

Some an ext examples:

### Example: 53 = 5 × 5 × 5 = 125

In words: 53 might be dubbed "5 come the 3rd power", "5 come the strength 3" or merely "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 power 4" or merely "2 come the 4th"

So in general:

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

## Another way of composing It

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

## Negative Exponents

Negative? What might be the contrary of multiplying? Dividing!

So we divide by the number each time, i m sorry is the very same as multiply by 1number

## Negative? flip the Positive!

 That last example showed one easier method to handle an adverse exponents: calculate the confident exponent (an)

More Examples:

an unfavorable Exponent reciprocal 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, climate 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 about 00 ? It might be one of two people 1 or 0, and so civilization say it is "indeterminate".

## It All provides Sense

If girlfriend look at the table, girlfriend will view that positive, zero ornegative exponents space really component of the exact 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..