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The exponent that a number says how countless times to usethe number in a multiplication.

You are watching: 2 to the power of negative 2

In this example: 82 = 8 × 8 = 64

In words: 82 deserve to be referred to as "8 to the second power", "8 to the strength 2" or merely "8 squared"

Example: 53 = 5 × 5 × 5 = 125

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


In general:

an tells you to use a in a multiplication n times:
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But those room positive exponents, what around something like:

8-2

That exponent is negative ... What does it mean?

Negative Exponents

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


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

Calculate the optimistic exponent (an)


negative ExponentReciprocal the Positive ExponentAnswer
4-2 = 1 / 42 = 1/16 = 0.0625
10-3 = 1 / 103 = 1/1,000 = 0.001

It All provides Sense

My favorite an approach is to start with "1" and also then multiply or divide as many times as the exponent says, then you will gain the best answer, for example:


Example: strength of 5
.. Etc..
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521 × 5 × 525
511 × 55
5011
5-11 ÷ 50.2
5-21 ÷ 5 ÷ 50.04
.. Etc..

See more: Snow White And The 7 Dwarfs Names, Seven Dwarfs


If friend look at the table, friend will check out that positive, zero or negative exponents room really part of the very same (fairly simple) pattern.