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

You are watching: What is 10 to the -2 power

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

In words: 82 can be referred to as "8 come the strength 2" or "8 to the 2nd power", or just "8 squared"

Exponents are likewise called strength or Indices.

Some more examples:


Example: 53 = 5 × 5 × 5 = 125

In words: 53 could be dubbed "5 to the third power", "5 to the strength 3" or merely "5 cubed"

Example: 24 = 2 × 2 × 2 × 2 = 16

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

So in general:

an speak you to multiply a by itself,so there space n of those a"s:
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Another method of creating It

Sometimes world use the ^ price (above the 6 on her keyboard), together it is straightforward to type.


Negative Exponents

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

So we divide by the number every time, i beg your pardon is the same as multiply by 1number


Negative? upper and lower reversal the Positive!

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

calculation the positive exponent (an)

More Examples:


an unfavorable 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, then you gain 1 (example 90 = 1)
But what around 00 ? It can be one of two people 1 or 0, and also so human being say that is "indeterminate".

It All makes Sense

If friend look at the table, girlfriend will view that positive, zero ornegative exponents space really component of the same (fairly simple) pattern:


Example: powers 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..