The exponent the a number says how numerous times to use the number in a multiplication.

You are watching: -3 to the 6th power

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

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

Exponents are also called powers or Indices.

Some an ext examples:


Example: 53 = 5 × 5 × 5 = 125

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

Example: 24 = 2 × 2 × 2 × 2 = 16

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

So in general:

an speak you to multiply a by itself,so there space n the those a"s:
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Another means of writing It

Sometimes civilization use the ^ prize (above the 6 on her keyboard), as it is easy to type.


Negative Exponents

Negative? What could be opposing 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 example showed an easier means to handle an adverse exponents:

calculation the hopeful 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 chin (example 91 = 9)
0 If the exponent is 0, climate you get 1 (example 90 = 1)
But what about 00 ? It can be one of two people 1 or 0, and so civilization say that is "indeterminate".

It All renders Sense

If friend look at that table, you will see that positive, zero ornegative exponents are 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..