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

You are watching: -4 to the 4th power

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

In words: 82 can be dubbed "8 come the power 2" or "8 come the second power", or simply "8 squared"

Exponents are additionally called powers or Indices.

Some much more examples:

### Example: 53 = 5 × 5 × 5 = 125

In words: 53 could be dubbed "5 come the third power", "5 come the strength 3" or simply "5 cubed"

### Example: 24 = 2 × 2 × 2 × 2 = 16

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

So in general:

 an tells you to main point a by itself,so there room n the those a"s:

## Another method of writing It

Sometimes civilization use the ^ price (above the 6 on her keyboard), together it is straightforward to type.

## Negative Exponents

Negative? What could be opposing of multiplying? Dividing!

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

## Negative? flip the Positive!

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

More Examples:

negative Exponent reciprocal ofPositive 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 actually the number chin (example 91 = 9) 0 If the exponent is 0, then you obtain 1 (example 90 = 1) But what around 00 ? It might be either 1 or 0, and also so world say the is "indeterminate".

## It All makes Sense

If you look at that table, girlfriend will view that positive, zero ornegative exponents are really component of the very same (fairly simple) pattern:

Example: powers of 5
.. Etc..

See more: Which Of The Following Sentences Contains A Dangling Modifier ?

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