The exponent of a number states how countless times to usage the number in a multiplication.

You are watching: What is 3 to the power of 5

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In 82 the "2" claims to usage 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 to the second 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 referred to as "5 to the third power", "5 come the strength 3" or simply "5 cubed"

Example: 24 = 2 × 2 × 2 × 2 = 16

In words: 24 might be dubbed "2 come the 4th power" or "2 come the strength 4" or merely "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 writing It

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


Negative Exponents

Negative? What might be opposing of multiplying? Dividing!

So we division by the number each time, which is the exact same as multiply by 1number


Negative? upper and lower reversal the Positive!

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That last instance showed one easier way to handle negative exponents:

calculation the hopeful exponent (an)

More Examples:


an unfavorable Exponent mutual 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, then you obtain 1 (example 90 = 1)
But what about 00 ? It can be one of two people 1 or 0, and also so human being say that is "indeterminate".

It All makes Sense

If girlfriend look at the table, you will check out that positive, zero ornegative exponents room really component of the very same (fairly simple) pattern:


Example: strength of 5
.. Etc..

See more: How Much Does A Small House Weigh ? (9 Easy Examples)

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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..