Math Doubts

Zero Exponent Power Rule

Formula

$\large b^0 = 1$

Proof

$b$ is a literal number. Assume, it is raised to power of zero to represent a quantity and it is written as $b^0$ algebraically.

The product of any number with one is equal to the same number. Hence, express $b$ raised the power of zero as the product of $1$ and $b$ raised the power of $0$.

$b^{\displaystyle 0} = 1 \times b^{\displaystyle 0}$

The meaning of $b^0$ is, write the literal $b$ zero times, which means no need to write it.

$\therefore \,\,\,\,\,\, b^{\displaystyle 0} = 1$

The value of any base number raised to the power of zero is always equal to one. Hence, the property called the zero power rule of exponents.

Example

$8^{\displaystyle 0}$ is an exponential term, having $8$ as base and zero as exponent.

$\implies 8^{\displaystyle 0} = 1 \times 8^{\displaystyle 0} $

$\implies 8^{\displaystyle 0} = 1$

Not only the value of $8^{\displaystyle 0}$, the value of any number which contains zero as its exponent is always one.



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