The exponent that a number states how countless times to use the number in a multiplication.

You are watching: 10 to the power of -3

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

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

Exponents are additionally called powers or Indices.

Some an ext examples:


Example: 53 = 5 × 5 × 5 = 125

In words: 53 might be dubbed "5 come the 3rd power", "5 come the strength 3" or merely "5 cubed"

Example: 24 = 2 × 2 × 2 × 2 = 16

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

So in general:

an tells you to multiply a by itself,so there are n the those a"s:
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Another way of composing It

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


Negative Exponents

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

So we divide by the number each time, i m sorry is the very same as multiply by 1number


Negative? flip the Positive!

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

calculate the confident 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, 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 about 00 ? It might be one of two people 1 or 0, and so civilization say it is "indeterminate".

It All provides Sense

If girlfriend look at the table, girlfriend will view that positive, zero ornegative exponents space really component of the exact 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..