1Cademy - Zero Exponent

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Quotient Property for Exponents

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Zero Exponent

The Zero Exponent rule states that any nonzero base raised to the zero power equals $1$ . If $a$ is a real number and $a \neq 0$ , then:

$a^0 = 1$

This result emerges naturally from the Quotient Property for Exponents. When a power is divided by itself — for example, $\frac{a^m}{a^m}$ — two conclusions follow simultaneously: the Quotient Property gives $a^{m-m} = a^0$ , and any nonzero quantity divided by itself equals $1$ . Setting these equal yields $a^0 = 1$ . The restriction $a \neq 0$ is essential because $0^0$ is indeterminate — the expression has no single agreed-upon value.

Regardless of the base — whether it is a whole number like $17$ , a variable like $x$ , or an expression like $(2x + 3)$ — as long as it is nonzero, raising it to the zero power always produces $1$ .

Updated 2026-04-29

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