🔑 Key Concepts
- As an exponent decreases by 1, the value is divided by the base.
- Any nonzero number raised to the zero power equals 1.
- The zero exponent rule follows the pattern established by positive exponents.
- When dividing powers with the same base, subtract the exponents.
- A nonzero quantity divided by itself always equals 1.
- The expression zero raised to the zero power is not included in the zero exponent rule.
✏️ Worked Examples – Why a Nonzero Number to the Zero Power Equals One
🧠 Math Vocabulary
- Base: The repeated factor in an exponential expression.
- Exponent: The number that indicates how many times the base is used as a factor.
- Zero Exponent: An exponent of zero that gives a value of 1 when the base is nonzero.
- Quotient of Powers: The rule stating that exponents are subtracted when powers with the same base are divided.
- Pattern: A predictable relationship that continues according to a rule.
- Nonzero: Any number or quantity that does not equal zero.
💡 Main Idea
Any nonzero number raised to the zero power equals 1. This can be explained by following exponent patterns or by applying the quotient rule. As an exponent decreases by 1, the value is divided by the base. The quotient rule also shows that dividing a power by itself produces an exponent of zero, while the original quantity divided by itself equals 1.
📚 What You Should Already Know
Before this lesson, students should understand positive exponents as repeated multiplication, recognize bases and exponents, and know how to divide powers with the same base by subtracting their exponents. Students should also understand that any nonzero quantity divided by itself equals 1.
🚀 What Comes Next
After understanding the zero exponent rule, students can extend the exponent pattern to negative exponents, rewrite negative powers as reciprocals, and simplify expressions that combine product, quotient, zero, and negative exponent rules.
🧩 Embed This Video in Your LMS
Teachers can embed this YouTube video directly into Canvas, Google Classroom, Schoology, or another learning platform. Click below to show the embed code.