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 $y \neq 0$.

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

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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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