Math Doubts

Zero Power Rule

Formula

$b^0 \,=\, 1$

The zero exponent with any base is equal to one, is called the zero power rule.

Introduction

The meaning of a number raise to the power zero is to write the number zero times but its value is one.

Take, $b$ is a literal and $b$ raised to the power of zero is written as $b^0$ in exponential notation. The value of $b$ raised to the power of zero is equal to one.

$b^0 \,=\, 1$

This identity in exponential form is called as zero exponent rule or zero power rule.

Examples

In this case, the literal $b$ can be any constant.

$(1) \,\,\,\,\,\,$ $3^0 \,=\, 1$

$(2) \,\,\,\,\,\,$ $e^0 \,=\, 1$

$(3) \,\,\,\,\,\,$ $x^0 \,=\, 1$

Proof

Learn how to derive the power rule for zero exponent in algebraic form.

Verification

$8^0$ is an exponential term. $8$ is base and zero is its exponent.

The product of one and any exponential term is equal to same exponential term.

$\implies$ $8^0 \,=\, 1 \times 8^0$

Now, write the number $1$ and write the base number $8$ zero times.

$\implies$ $8^0 \,=\, 1$

Therefore, it is verified that any number raised to the power of zero is always equal to one.

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