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

You are watching: 5 to the power of -3

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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 to the strength 2" or "8 to the 2nd power", or merely "8 squared"

Exponents are likewise called strength or Indices.

Some much more examples:


Example: 53 = 5 × 5 × 5 = 125

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

Example: 24 = 2 × 2 × 2 × 2 = 16

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

So in general:

an tells you to multiply a through itself,so there room n the those a"s:
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Another way of composing It

Sometimes human being use the ^ prize (above the 6 on your keyboard), together it is straightforward to type.


Negative Exponents

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

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


Negative? upper and lower reversal the Positive!

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

calculate the optimistic exponent (an)

More Examples:


an adverse 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, then you just have the number itself (example 91 = 9)
0 If the exponent is 0, climate you obtain 1 (example 90 = 1)
But what around 00 ? It could be either 1 or 0, and so civilization say it is "indeterminate".

It All renders Sense

If friend look at the table, you will view 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..