Lesson 7: More Properties of Exponents

Property

$a^0 = 1$, if $a \neq 0$

This definition is based on the second law of exponents. For any non-zero number $a$, the quotient $\frac{a^n}{a^n}$ is equal to 1. Using the law of exponents, we can also write $\frac{a^n}{a^n} = a^{n-n} = a^0$. Therefore, it is logical to define $a^0$ as 1.

Examples

• For a positive integer, $8^0 = 1$.
• For a negative integer, $(-55)^0 = 1$.
• For an algebraic term where variables are non-zero, $(2ab^2)^0 = 1$.

Property

As the exponent of a base decreases by 1, the value of the power is divided by the base. This pattern can be extended from positive exponents to zero and negative exponents to understand their meaning.

Examples