1. The problem: Understand and describe the exponent rules. 2. Exponent rules are formulas that help simplify expressions involving powers of numbers or variables. 3. Key exponent rules include: - Product rule: $$a^m \times a^n = a^{m+n}$$ (When multiplying with the same base, add the exponents.) - Quotient rule: $$\frac{a^m}{a^n} = a^{m-n}$$ (When dividing with the same base, subtract the exponents.) - Power rule: $$(a^m)^n = a^{m \times n}$$ (When raising a power to another power, multiply the exponents.) - Zero exponent rule: $$a^0 = 1$$ (Any nonzero base raised to zero is 1.) - Negative exponent rule: $$a^{-n} = \frac{1}{a^n}$$ (A negative exponent means reciprocal.) - Power of a product: $$(ab)^n = a^n b^n$$ (Distribute the exponent to each factor.) - Power of a quotient: $$\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}$$ (Distribute the exponent to numerator and denominator.) 4. These rules help simplify expressions and solve equations involving exponents efficiently. 5. Always remember the base must be the same to apply product and quotient rules. 6. Practice applying these rules to become comfortable with exponent operations.