The exponent of a number claims how numerous times to use the number in a multiplication.

You are watching: What is 6 to the power of 3

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

Exponents are likewise called strength or Indices.

Some more examples:


Example: 53 = 5 × 5 × 5 = 125

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

Example: 24 = 2 × 2 × 2 × 2 = 16

In words: 24 could be called "2 come the fourth power" or "2 come the power 4" or merely "2 come the 4th"

So in general:

an tells you to main point a by itself,so there space n that those a"s:
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Another means of writing It

Sometimes world use the ^ prize (above the 6 on your keyboard), as it is straightforward to type.


Negative Exponents

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

So we division by the number each time, i m sorry is the exact same as multiplying by 1number


Negative? upper and lower reversal the Positive!

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That last example showed an easier method to handle negative exponents:

calculate the hopeful exponent (an)

More Examples:


negative 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, then you just have actually the number itself (example 91 = 9)
0 If the exponent is 0, then you get 1 (example 90 = 1)
But what about 00 ? It can be one of two people 1 or 0, and also so world say that is "indeterminate".

It All renders Sense

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


Example: strength 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..