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

You are watching: -4 to the 4th power

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

In words: 82 can be dubbed "8 come the power 2" or "8 come the second power", or simply "8 squared"

Exponents are additionally called powers or Indices.

Some much more examples:


Example: 53 = 5 × 5 × 5 = 125

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

Example: 24 = 2 × 2 × 2 × 2 = 16

In words: 24 might be called "2 come the 4th power" or "2 to the strength 4" or just "2 to the 4th"

So in general:

an tells you to main point a by itself,so there room n the those a"s:
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Another method of writing It

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


Negative Exponents

Negative? What could be opposing of multiplying? Dividing!

So we divide by the number every time, which is the very 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:

calculate the positive exponent (an)

More Examples:


negative Exponent reciprocal ofPositive Exponent answer
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, then you just have actually the number chin (example 91 = 9)
0 If the exponent is 0, then you obtain 1 (example 90 = 1)
But what around 00 ? It might be either 1 or 0, and also so world say the is "indeterminate".

It All makes Sense

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


Example: powers of 5
.. Etc..

See more: Which Of The Following Sentences Contains A Dangling Modifier ?

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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..