The exponent of a number states just how many times to use the number in a multiplication.

You are watching: 5 to the power of 5

*

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

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

Exponents are likewise called Powers or Indices.

Some even more examples:


Example: 53 = 5 × 5 × 5 = 125

In words: 53 might be called "5 to the 3rd power", "5 to the power 3" or ssuggest "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 power 4" or sindicate "2 to the 4th"

You have the right to multiply any number by itself as many kind of times as you desire making use of exponents.

Try here:

In General

So in general:

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

Anvarious other Way of Writing It

Sometimes civilization use the ^ symbol (above the 6 on your keyboard), as it is basic to type.

See more: " American Experience The Swamp (Tv Episode 2019), American Experience The Swamp (Tv Episode 2019)


Negative Exponents

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

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


Negative? Flip the Positive!

*

That last example verified an simpler method to manage negative exponents:

Calculate the positive exponent (an)

More Examples:


Negative ExponentReciprocal ofConfident ExponentAnswer
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?

1If the exponent is 1, then you simply have the number itself (instance 91 = 9)
0If the exponent is 0, then you get 1 (example 90 = 1)
But what about 00 ? It could be either 1 or 0, and so civilization say it is "indeterminate".

It All Makes Sense

If you look at that table, you will see that positive, zero or negative exponents are really component of the exact same (reasonably simple) pattern: