Zero Exponent Rule
See It in Action
Two examples of the idea done right—and one common look-alike that is not right.
EXAMPLE
EXAMPLE
NON-EXAMPLE
Definition
The Zero Exponent Rule states that any non-zero number raised to the power of zero is equal to 1. Mathematically, this is written as:
a^0 = 1 for any a not equal to 0
Key Points:
The base a can be any non-zero number (whether it's a positive or negative number, a fraction, or a variable).
The exponent is 0.
The rule only applies when the base is not zero. Zero raised to the power of zero, 0^0, is indeterminate and does not follow this rule.
Examples:
1. Positive number:
5^0 = 1
2. Negative number:
(-3)^0 = 1
3. Fraction:
(2/7)^0=1
4. Variable:
x^0 = 1 as long as x does not equal 0
Why does this work?
The zero exponent rule can be understood through the Product of Powers Property of exponents, which states:
a^m • a^n = a^(m + n)
If we set m = n and consider the case when m = 1, we get:
a^1 • a^0 = a^(1 + 0) = a^1
But since a^1 = a, we can divide both sides by a (assuming a does not equal 0):
a^0 = 1
Thus, the zero exponent rule is consistent with the laws of exponents.
Conclusion:
The Zero Exponent Rule simplifies expressions where any non-zero number or variable is raised to the power of zero, resulting in 1.