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The exponent of a number claims how many kind of times to usethe number in a multiplication.

You are watching: 5 to the power of

In this example: 82 = 8 × 8 = 64

In words: 82 have the right to be dubbed "8 to the second power", "8 to the power 2" or sindicate "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 sindicate "5 cubed"


In general:

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

8-2

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

Negative Exponents

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


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That last instance confirmed an much easier method to take care of 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 technique is to begin through "1" and then multiply or divide as many type of times as the exponent says, then you will certainly obtain the appropriate answer, for example:


Example: Powers of 5
.. and so on.
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521 × 5 × 525
511 × 55
5011
5-11 ÷ 50.2
5-21 ÷ 5 ÷ 50.04
.. and so on.

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