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The exponent of a number says how many 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 can be called "8 to the second power", "8 to the power 2" or simply "8 squared"

Example: 53 = 5 × 5 × 5 = 125

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


In general:

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

8-2

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

Negative Exponents

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


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

Calculate the positive exponent (an)


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

It All Makes Sense

My favorite method is to start with "1" and then multiply or divide as many times as the exponent says, then you will get the right answer, for example:


Example: Powers 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 you look at that table, you will see that positive, zero or negative exponents are really part of the same (fairly simple) pattern.