📖Definition
An exponent tells you how many times to multiply a number (the base) by itself. In the expression aⁿ, a is the base and n is the exponent. For example, 2³ means 2 × 2 × 2 = 8.
📐Formula
aⁿ = a × a × a × ... (n times)
The base a is multiplied by itself n times. For example, 5² = 5 × 5 = 25, and 2⁴ = 2 × 2 × 2 × 2 = 16.
📝Step-by-Step Guide
1
Product Rule
When multiplying same bases, add the exponents.
aᵐ × aⁿ = aᵐ⁺ⁿ
2
Quotient Rule
When dividing same bases, subtract the exponents.
aᵐ ÷ aⁿ = aᵐ⁻ⁿ
3
Power Rule
When raising a power to a power, multiply the exponents.
(aᵐ)ⁿ = aᵐˣⁿ
4
Special Cases
Zero exponent: a⁰ = 1 (when a ≠ 0). Negative exponent: a⁻ⁿ = 1/aⁿ.
a⁰ = 1; a⁻ⁿ = 1/aⁿ
⚠️Common Mistakes to Avoid
- Adding exponents when you should multiply bases
- Confusing the product and power rules
- Thinking a⁰ equals 0 (it equals 1)
- Incorrectly handling negative exponents
- Applying exponent rules to different bases
✏️Practice Problems
Easy
Simplify 2³ × 2²
Answer: 2⁵ = 32
Medium
Simplify (3²)³
Answer: 3⁶ = 729
Hard
Simplify (2³ × 2⁻¹)² ÷ 2²
Answer: 2² = 4
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Worked Examples
🔗Related Topics
Curriculum Alignment
CommonCore (8.EE.A.1)KS3KMK