The exponent that a number claims how numerous 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" states to use 8 double in a multiplication,so 82 = 8 × 8 = 64

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

Exponents are also called strength or Indices.

Some an ext examples:


Example: 53 = 5 × 5 × 5 = 125

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

Example: 24 = 2 × 2 × 2 × 2 = 16

In words: 24 can be referred to as "2 to the fourth 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 the those a"s:
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Another method of creating It

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


Negative Exponents

Negative? What might 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 an easier way to handle an unfavorable exponents:

calculate the positive exponent (an)

More Examples:


negative 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, climate you just have actually the number chin (example 91 = 9)
0 If the exponent is 0, then you get 1 (example 90 = 1)
But what about 00 ? It can be either 1 or 0, and also so people say the is "indeterminate".

It All makes Sense

If you look at the table, you will watch 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..