The exponent that a number claims how countless times to usage the number in a multiplication.

You are watching: What is 3 to the 6th power

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

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

Exponents are also called strength or Indices.

Some more examples:


Example: 53 = 5 × 5 × 5 = 125

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

Example: 24 = 2 × 2 × 2 × 2 = 16

In words: 24 could be called "2 come the fourth power" or "2 come the strength 4" or just "2 come the 4th"

So in general:

an speak you to main point a by itself,so there space n of those a"s:
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Another way of writing It

Sometimes people use the ^ symbol (above the 6 on your keyboard), together it is straightforward to type.


Negative Exponents

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

So we division by the number every time, which is the same as multiplying by 1number


Negative? upper and lower reversal the Positive!

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That last example showed one easier means to handle negative exponents:

calculation the optimistic 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 itself (example 91 = 9)
0 If the exponent is 0, then you acquire 1 (example 90 = 1)
But what about 00 ? It might be either 1 or 0, and so world say it is "indeterminate".

It All provides Sense

If friend look at the table, girlfriend will see that positive, zero ornegative exponents room really part of the 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..