What does a number ex. 18 to the 0 power equal? Help! Does it equal 1? I think so but I'm not sure. Help!

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ishpiro's profile pic

ishpiro | College Teacher | (Level 1) Educator

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Any number (except for 0), when raised to the power of 0, equals 1:

`2^0 = 1`

`18^0 = 1`

`1000^0 = 1`

and so on.

To understand why this has to be the case, consider the definition to exponent and how it applies to any given number. For example, for number 3

`3^1 = 3`

`3^2 = 3*3 = 9`

`3^3 = 3*3*3 = 27`

Notice that as each exponent decreases by 1, for example, from 3 to 2, each results gets divided by 3: 27/3 = 9.

Similarly, when exponent of 3 goes down from 2 to 1, the result is divided by 3: 9/3 = 3.

To continue this pattern to include the exponent of 0, the exponent 1 would have to decrease by 1: 1 - 1 = 0. This means the first power of 3, 3, would have to be divided by 3: 3/3 = 1. Therefore, `3^0 = 1` .

So, the fact that 0th power of any number is 1 is consistent with the definition of exponent.

Thus, `18^0 = 1` .

ssarfraz's profile pic

ssarfraz | Student, Professional | (Level 2) Honors

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According to the rules of maths, Any number with power 0 is equal to 1 except for one case in which 0 power 0 is equal to 0 instead of 1.

Hence you are right.

malkaam's profile pic

malkaam | Student, Undergraduate | (Level 1) Valedictorian

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Yes, you are correct. Any number with the power of 0 is equal to 1, whereas only 0 raised to the power 0 is not 1.

tonys538's profile pic

tonys538 | Student, Undergraduate | (Level 1) Valedictorian

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When dealing with expressions that have exponents some formulas that are commonly used are:

x^(a+b) = x^a*x^b

x^(a - b) = x^a/x^b

(x^a)^b = x^(a*b)

If a number is raised to the power 0, 0 can be written as the difference of 2 equal numbers. For example, 0 = 2 - 2

Now if a number is raised to the power 0, for example 8^0 using the formula given above: 8^0 = 8^(2 - 2)

= 8^2/8^2

= 1

This is one way of showing that any number except 0 raised to the power 0 gives 1. Note that 0 raised to the power 0 is not defined as 0/0 is indeterminate.

rachellopez's profile pic

rachellopez | Student, Grade 12 | (Level 1) Valedictorian

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It is a math rule that any number raised to the power of 0, except 0 itself, equals 1. The easiest way to look at it is, each time the exponent decreases by 1, you are dividing by your base number one time.

Ex. 5^3 = 5*5*5 = 125

      5^2 = 5*5    = 25

      5^1              = 5 

      5^0              = 1

Here, when you have 5 to the third power you get 125. Now, decrease the power by 1 and you have 5 squared. If you divide 125 by 5 you get that 5 squared equals 25. Same thing if you divide 25 by 5 you get 5 which is equal to 5 to the first power. In order for the pattern to continue 5 divided by 5 equals 1, which is 5 to the 0 power. 

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