The zero exponent

Next, let’s look at the division [[$ \dfrac{4^3}{4^3} $]] in two different ways. Let's simplify by the quotient of equal powers and by reducing.

Since both actions are allowed, the results must be equal. In other words, [[$ 4^0 = 1 $]].

Zero as an exponent

If there is a zero as an exponent, the value of the power is always 1. The base number can never be zero.

[[$ a^0 = 1 \text{, kun } a \neq 0. $]]

Example 3

Simplify the powers.

a) [[$ 99^0 = 1 $]]

b) [[$ -45^0 = -1 $]]

c) [[$ 0^0 $]] cannot be calculated

d) [[$ \dfrac{a^3 \cdot a^9}{a^{12}} = \dfrac{a^{3+9}}{a^{12}} = \dfrac{a^{12}}{a^{12}} = a^{12-12} =a^0 = 1 $]]