The exponent that a number states how plenty of times to usage the number in a multiplication.

You are watching: What is 2 to the 4th power

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

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

Exponents are additionally called strength or Indices.

Some much more examples:


Example: 53 = 5 × 5 × 5 = 125

In words: 53 might be referred to as "5 to the 3rd power", "5 to the power 3" or simply "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 to the 4th"

So in general:

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

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


Negative Exponents

Negative? What might be opposing of multiplying? Dividing!

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


Negative? upper and lower reversal the Positive!

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That last example showed an easier way to handle an unfavorable exponents:

calculation the hopeful exponent (an)

More Examples:


negative Exponent mutual 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 itself (example 91 = 9)
0 If the exponent is 0, climate you gain 1 (example 90 = 1)
But what about 00 ? It could be one of two people 1 or 0, and also so world say it is "indeterminate".

It All makes Sense

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


Example: powers of 5
.. Etc..

See more: How Many Cups In 32 Ounce - Ounces To Cups Converter (Oz To Cups)

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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..