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

You are watching: 6 to the power of 5

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

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

Exponents are also called strength or Indices.

Some more examples:


Example: 53 = 5 × 5 × 5 = 125

In words: 53 can be referred to as "5 to the 3rd power", "5 to the strength 3" or just "5 cubed"

Example: 24 = 2 × 2 × 2 × 2 = 16

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

So in general:

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

Sometimes world use the ^ price (above the 6 on your keyboard), as it is straightforward to type.


Negative Exponents

Negative? What could be the contrary 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 an easier way to handle negative exponents:

calculate the positive exponent (an)

More Examples:


an unfavorable 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 could be one of two people 1 or 0, and also so world say it is "indeterminate".

It All renders Sense

If girlfriend look at that table, you will check out that positive, zero ornegative exponents space really part 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..