Properties of Exponents

Exponents are repeated multiplication

2⁴ means 2 × 2 × 2 × 2 = 16. The base is 2 and the exponent is 4.

The key rules

1. 1Product rule: same base, add exponents - x³ · x² = x⁵.
2. 2Quotient rule: same base, subtract exponents - x⁵ ÷ x² = x³.
3. 3Power rule: power of a power, multiply exponents - (x³)² = x⁶.
4. 4Zero exponent: any nonzero base to the 0 power is 1.

Why this matters

Use the product, quotient, and power rules to simplify expressions.

These ideas show up on homework, quizzes, and the next unit in this grade. Getting comfortable here saves time later when the problems stack more steps together.

Common mistakes to avoid

Doing different operations to each side of an equation. Whatever you add, subtract, multiply, or divide on one side, do to the other.

Combining unlike terms (like 3x and 4) as if they were the same kind of term.

Key ideas from this lesson

1. Exponents are repeated multiplication
2. The key rules
3. Product rule: same base, add exponents - x³ · x² = x⁵.
4. Quotient rule: same base, subtract exponents - x⁵ ÷ x² = x³.
5. Power rule: power of a power, multiply exponents - (x³)² = x⁶.
6. Zero exponent: any nonzero base to the 0 power is 1.