$b^0 \,=\, 1$

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

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.

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

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

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

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

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

$8^0$ 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.

Latest Math Topics

Jul 24, 2022

Jul 15, 2022

Latest Math Problems

Jul 29, 2022

Jul 17, 2022

Jun 02, 2022

Apr 06, 2022

A best free mathematics education website for students, teachers and researchers.

Learn each topic of the mathematics easily with understandable proofs and visual animation graphics.

Learn how to solve the maths problems in different methods with understandable steps.

Copyright © 2012 - 2022 Math Doubts, All Rights Reserved