The exponent of a number states exactly how many type of times to usage the number in a multiplication.

You are watching: -2 to the power of -2

*

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

In words: 82 can be referred to as "8 to the power 2" or "8 to the second power", or simply "8 squared"

Exponents are likewise called Powers or Indices.

Some more examples:


Example: 53 = 5 × 5 × 5 = 125

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

Example: 24 = 2 × 2 × 2 × 2 = 16

In words: 24 could be dubbed "2 to the fourth power" or "2 to the power 4" or ssuggest "2 to the 4th"

So in general:

an tells you to multiply a by itself,so tright here are n of those a"s:
*

Another Way of Writing It

Sometimes human being usage the ^ symbol (over the 6 on your keyboard), as it is basic to type.


Negative Exponents

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

So we divide by the number each time, which is the very same as multiplying by 1number


Negative? Flip the Positive!

*

That last example verified an easier means to handle negative exponents:

Calculate the positive exponent (an)

More Examples:


Negative Exponent Reciprocal ofOptimistic 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 the number itself (example 91 = 9)
0 If the exponent is 0, then you gain 1 (example 90 = 1)
But what around 00 ? It could be either 1 or 0, and also so world say it is "indeterminate".

It All Makes Sense

If you look at that table, you will check out that positive, zero ornegative exponents are really part of the exact same (reasonably simple) pattern:


Example: Powers of 5
.. and so on..

See more: The Sl I Believe I Might Be Of Service Gifs, David Bowie Is Of Service Gif

*
52 5 × 5 25
51 5 5
50 1 1
5-1 15 0.2
5-2 15 × 15 0.04
.. and so on.