What to do when the exponent is zero

 
 
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What do you do with a zero exponent?

This lesson will cover how to find the power of a number or nonzero variable raised to the zero power.

The rule for zero as an exponent:

Any nonzero real number raised to the power of zero is one, this means anything that looks like ???a^0??? will always equal ???1??? if ???a??? is not equal to zero.

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What is a constant raised to the zero power?

Example

Simplify the expression.

???9^0???

 

Just remember that any nonzero real number raised to the power of zero is one, so

???9^0 = 1???

 
 
 

Video with lots of examples of different kinds of numbers raised to the zero power

 

 
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What is a really big number raised to the 0 power equal to?

Example

Simplify the expression.

???99,102^0???

 

Look different? Don’t worry, just remember that any nonzero real number raised to the power of zero is one, so

???99,102^0=1???

 
 
zero as an exponent

Just remember that any nonzero real number raised to the power of zero is one

 
 

What do you get when you raise a variable to the power of zero?

Example

Simplify the expression.

???y^0???

 

It’s still true that any nonzero real number raised to the power of zero is one so,

???y^0=1???

We do need to assume that ???y \neq 0???.


Good news, the rule is still true if you have more than one variable, or a combination of variables and numerals.


Raising an expression to the zero power

Example

Simplify the expression.

???(3xy + a)^0???

 

It’s still true that any nonzero real number raised to the power of zero is one and we know that ???3xy + a??? really is just a representation of a number. This means,

???(3xy + a)^0=1???

We do make the assumption that the expression ???3xy+a??? isn’t equal to ???0???.

 
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