Question
What is the Zero Power Rule in math?
Answers
GPT-4o mini
The Zero Power Rule in mathematics states that any non-zero number raised to the power of zero is equal to one. This can be expressed mathematically as:
\[ a^0 = 1 \]
for any \( a \neq 0 \).
For example:
- \( 5^0 = 1 \)
- \( (-3)^0 = 1 \)
- \( 100^0 = 1 \)
This rule is a result of the properties of exponents. Specifically, it arises from the division of powers:
\[ a^m \div a^m = a^{m-m} = a^0 \]
Since any non-zero number divided by itself equals 1, we have:
\[ a^0 = 1 \]
Note that the Zero Power Rule does not apply to zero itself, as \( 0^0 \) is considered indeterminate in many contexts.
\[ a^0 = 1 \]
for any \( a \neq 0 \).
For example:
- \( 5^0 = 1 \)
- \( (-3)^0 = 1 \)
- \( 100^0 = 1 \)
This rule is a result of the properties of exponents. Specifically, it arises from the division of powers:
\[ a^m \div a^m = a^{m-m} = a^0 \]
Since any non-zero number divided by itself equals 1, we have:
\[ a^0 = 1 \]
Note that the Zero Power Rule does not apply to zero itself, as \( 0^0 \) is considered indeterminate in many contexts.