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

You are watching: -2 to the 3rd power

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

In words: 82 could be dubbed "8 come the strength 2" or "8 to the 2nd power", or merely "8 squared"

Exponents are also called powers or Indices.

Some an ext examples:


Example: 53 = 5 × 5 × 5 = 125

In words: 53 could be referred to as "5 come the 3rd power", "5 come the power 3" or merely "5 cubed"

Example: 24 = 2 × 2 × 2 × 2 = 16

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

So in general:

an speak you to multiply a by itself,so there are n that those a"s:
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Another method of creating It

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


Negative Exponents

Negative? What could be opposing of multiplying? Dividing!

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


Negative? flip the Positive!

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That last example showed one easier way to handle an adverse exponents:

calculate the positive exponent (an)

More Examples:


an unfavorable 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, climate you get 1 (example 90 = 1)
But what around 00 ? It can be either 1 or 0, and also so human being say it is "indeterminate".

It All provides Sense

If friend look at the table, girlfriend will watch that positive, zero ornegative exponents space 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..