The exponent that a number says how plenty of times to usage the number in a multiplication.

You are watching: 2 to the power of -1

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

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

Exponents are likewise called powers or Indices.

Some more examples:


Example: 53 = 5 × 5 × 5 = 125

In words: 53 could be called "5 to the 3rd power", "5 come the power 3" or simply "5 cubed"

Example: 24 = 2 × 2 × 2 × 2 = 16

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

So in general:

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

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


Negative Exponents

Negative? What could be opposing of multiplying? Dividing!

So we division by the number every time, i m sorry is the exact same as multiplying by 1number


Negative? flip the Positive!

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That last example showed one easier means to handle an adverse exponents:

calculation the hopeful exponent (an)

More Examples:


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

It All makes Sense

If you look at the table, friend will see that positive, zero ornegative exponents room really component of the exact same (fairly simple) pattern:


Example: strength of 5
.. Etc..

See more: The Battle Of English And Mathematics Answer, The Battle Of English Vs

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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..