Zero as an exponent

Algebra 2

 
zero as an 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.

 
 

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???


Let’s look at another example.


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

 

Let’s try some examples with variables.


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.


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???.


Want to learn more about Algebra 2?

I have a step-by-step course for that. 😃


Krista King