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

You are watching: 2 to the power of -3

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In 82 the \"2\" states to usage 8 double in a multiplication,so 82 = 8 × 8 = 64

In words: 82 might be referred to as \"8 come the power 2\" or \"8 to the 2nd power\", or just \"8 squared\"

Exponents are additionally called powers or Indices.

Some more examples:


Example: 53 = 5 × 5 × 5 = 125

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

Example: 24 = 2 × 2 × 2 × 2 = 16

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

So in general:

an speak you to main point a by itself,so there room n that those a\"s:
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Another way of composing It

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


Negative Exponents

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

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


Negative? flip the Positive!

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That last instance showed an easier method to handle an adverse exponents:

calculation the optimistic 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 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 people say it is \"indeterminate\".

It All renders Sense

If you look at that table, friend will view that positive, zero ornegative exponents are really component of the very same (fairly simple) pattern:


Example: powers 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..