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

You are watching: -2 to the 6th power

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

In words: 82 can be referred to as "8 to the power 2" or "8 come the second power", or simply "8 squared"

Exponents are additionally called powers or Indices.

Some more examples:


Example: 53 = 5 × 5 × 5 = 125

In words: 53 might be referred to as "5 to the 3rd power", "5 come the strength 3" or simply "5 cubed"

Example: 24 = 2 × 2 × 2 × 2 = 16

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

So in general:

an tells you to main point a by itself,so there space n of those a"s:
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Another method of creating It

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


Negative Exponents

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

So we division by the number each time, i beg your pardon is the exact same as multiply by 1number


Negative? upper and lower reversal the Positive!

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

calculation the confident exponent (an)

More Examples:


negative 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 civilization say the is "indeterminate".

It All renders Sense

If friend look at the table, friend will see that positive, zero ornegative exponents are really component 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..