What to do when the exponent is zero
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???
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???.
