Lesson 4: Zero and Negative Exponents

Property

Zero Exponent Property
If $a$ is a non-zero number, then $a^0 = 1$.

Properties of Negative Exponents
If $n$ is an integer and $a \neq 0$, then $a^{-n} = \frac{1}{a^n}$ and $\frac{1}{a^{-n}} = a^n$.

Quotient to a Negative Power Property
If $a$ and $b$ are real numbers, $a \neq 0$, $b \neq 0$ and $n$ is an integer, then

Property

When simplifying expressions with like bases and zero or negative exponents:

• Product Rule: $a^m \cdot a^n = a^{m+n}$
• Quotient Rule: $\frac{a^m}{a^n} = a^{m-n}$
• These rules apply regardless of whether exponents are positive, negative, or zero

Examples

Property

In decimal place value, positions to the right of the decimal point are represented by negative powers of 10: