The zero power rule of exponents states that any non-zero number raised to the power of zero is equal to one. In mathematical terms, for any \( a \neq 0 \):
\[ a^0 = 1 \]
Here's how it breaks down:
- \( 5^0 = 1 \)
- \( (-3)^0 = 1 \)
- \( \left(\frac{1}{2}\right)^0 = 1 \)
- \( 100^0 = 1 \)
Let's practice some problems using the zero power rule. Here are a few questions and answers:
Practice Problems
- What is \( 7^0 \)?
- What is \( (-4)^0 \)?
- What is \( \left(\frac{2}{3}\right)^0 \)?
- What is \( 0^0 \)? (Note: This is a special case, often considered indeterminate in mathematics)
Answers
- \( 7^0 = 1 \)
- \( (-4)^0 = 1 \)
- \( \left(\frac{2}{3}\right)^0 = 1 \)
- \( 0^0 \) is often debated and is generally treated as indeterminate.
Additional Questions
Try these on your own:
- What is \( 12^0 \)?
- \( x^0 \) (where \( x \) is any non-zero number)?
- What is \( (8.5)^0 \)?
- If \( a = 15 \), what is \( a^0 \)?
Answers for Additional Questions
- \( 12^0 = 1 \)
- \( x^0 = 1 \) (as long as \( x \neq 0 \))
- \( (8.5)^0 = 1 \)
- \( a^0 = 1 \) (since \( a = 15 \), \( 15^0 = 1 \))
Feel free to reach out if you have more questions or need further explanations!