# WHAT IS 3 TO THE FOURTH POWER

The exponent of a number says how many times lớn use the number in a multiplication.

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

In words: 82 could be called "8 to lớn the nguồn 2" or "8 to lớn the second power", or simply "8 squared"

Exponents are also called Powers or Indices.

Some more examples:

### Example: 53 = 5 × 5 × 5 = 125

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

### Example: 24 = 2 × 2 × 2 × 2 = 16

In words: 24 could be called "2 to the fourth power" or "2 lớn the power 4" or simply "2 to the 4th"

So in general:

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

## Another Way of Writing It

Sometimes people use the ^ symbol (above the 6 on your keyboard), as it is easy khổng lồ type.

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## Negative Exponents

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

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

## Negative? Flip the Positive!

 That last example showed an easier way khổng lồ handle negative 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 the number itself (example 91 = 9) 0 If the exponent is 0, then you get 1 (example 90 = 1) But what about 00 ? It could be either 1 or 0, và so people say it is "indeterminate".

## It All Makes Sense

If you look at that table, you will see that positive, zero ornegative exponents are really part of the 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..