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

You are watching: -5 to the 4th power

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

In words: 82 could be called "8 come the strength 2" or "8 come the second power", or merely "8 squared"

Exponents are also called powers or Indices.

Some much more examples:


Example: 53 = 5 × 5 × 5 = 125

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

Example: 24 = 2 × 2 × 2 × 2 = 16

In words: 24 might be referred to as "2 to the fourth power" or "2 to the strength 4" or just "2 to the 4th"

So in general:

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

Sometimes civilization use the ^ prize (above the 6 on your keyboard), together it is easy to type.


Negative Exponents

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

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


Negative? upper and lower reversal the Positive!

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That last instance showed one easier way to handle an unfavorable exponents:

calculate the confident exponent (an)

More Examples:


an adverse Exponent mutual ofPositive Exponent prize
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 the number itself (example 91 = 9)
0 If the exponent is 0, climate you acquire 1 (example 90 = 1)
But what around 00 ? It might be either 1 or 0, and also so human being say it is "indeterminate".

It All provides Sense

If you look at the table, friend will see that positive, zero ornegative exponents room really part 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..