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

You are watching: What is 3 to the power of 4

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

In words: 82 might be referred to as "8 come the power 2" or "8 come the 2nd power", or merely "8 squared"

Exponents are also called strength or Indices.

Some an ext examples:


Example: 53 = 5 × 5 × 5 = 125

In words: 53 might be referred to as "5 to the third power", "5 come the power 3" or merely "5 cubed"

Example: 24 = 2 × 2 × 2 × 2 = 16

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

So in general:

an speak you to multiply a by itself,so there room n of those a"s:
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Another way of writing It

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


Negative Exponents

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

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


Negative? flip the Positive!

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That last example showed one easier way to handle negative exponents:

calculation the optimistic exponent (an)

More Examples:


an unfavorable Exponent reciprocal 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 the number itself (example 91 = 9)
0 If the exponent is 0, climate you gain 1 (example 90 = 1)
But what about 00 ? It could be one of two people 1 or 0, and so civilization say that is "indeterminate".

It All provides Sense

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


Example: powers of 5
.. Etc..

See more: How Many Liters Is 12 Ounces To Liters Conversion Calculator

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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..