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

You are watching: -3 to the 4th power

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

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

Exponents are likewise called powers or Indices.

Some more examples:


Example: 53 = 5 × 5 × 5 = 125

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

Example: 24 = 2 × 2 × 2 × 2 = 16

In words: 24 might be referred to as "2 come the fourth 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 of those a"s:
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Another method of writing It

Sometimes human being use the ^ price (above the 6 on her keyboard), as it is simple to type.


Negative Exponents

Negative? What could be opposing of multiplying? Dividing!

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


Negative? flip the Positive!

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That last example showed one easier way to handle negative exponents:

calculation the optimistic exponent (an)

More Examples:


an adverse Exponent mutual 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, then you just have actually the number chin (example 91 = 9)
0 If the exponent is 0, then you gain 1 (example 90 = 1)
But what around 00 ? It can be one of two people 1 or 0, and also so world say it is "indeterminate".

It All provides Sense

If girlfriend look at that table, girlfriend will check out 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..