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

You are watching: -2 to the fourth power

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

In words: 82 might be dubbed "8 come the strength 2" or "8 come the 2nd power", or just "8 squared"

Exponents are additionally called powers or Indices.

Some much more examples:


Example: 53 = 5 × 5 × 5 = 125

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

Example: 24 = 2 × 2 × 2 × 2 = 16

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

So in general:

an tells you to main point a through itself,so there space n that those a"s:
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Another way of creating It

Sometimes civilization use the ^ symbol (above the 6 on your keyboard), together it is basic to type.


Negative Exponents

Negative? What can be opposing of multiplying? Dividing!

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


Negative? flip the Positive!

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That last instance showed one easier way to handle an unfavorable exponents:

calculation the confident exponent (an)

More Examples:


an unfavorable Exponent reciprocal ofPositive Exponent price
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, climate you just have the number chin (example 91 = 9)
0 If the exponent is 0, climate you obtain 1 (example 90 = 1)
But what about 00 ? It can be either 1 or 0, and also so people say that is "indeterminate".

It All renders Sense

If girlfriend look at that table, girlfriend will see that positive, zero ornegative exponents space really part of the very 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..