The exponent of a number states exactly how many type of times to usage the number in a multiplication.

You are watching: -2 to the power of -2

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 to the power 2" or "8 to the second power", or simply "8 squared"

Exponents are likewise called Powers or Indices.

Some more examples:

### Example: 53 = 5 × 5 × 5 = 125

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

### Example: 24 = 2 × 2 × 2 × 2 = 16

In words: 24 could be dubbed "2 to the fourth power" or "2 to the power 4" or ssuggest "2 to the 4th"

So in general:

 an tells you to multiply a by itself,so tright here are n of those a"s:

## Another Way of Writing It

Sometimes human being usage the ^ symbol (over the 6 on your keyboard), as it is basic to type.

## Negative Exponents

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

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

## Negative? Flip the Positive!

 That last example verified an easier means to handle negative exponents: Calculate the positive exponent (an)

More Examples:

Negative Exponent Reciprocal ofOptimistic Exponent Answer
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, then you gain 1 (example 90 = 1) But what around 00 ? It could be either 1 or 0, and also so world say it is "indeterminate".

## It All Makes Sense

If you look at that table, you will check out that positive, zero ornegative exponents are really part of the exact same (reasonably simple) pattern:

Example: Powers of 5
.. and so on..

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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
.. and so on.