1. The problem: Understand and describe the exponent rules. 2. Exponent rules are formulas that help us simplify expressions involving powers. 3. Key exponent rules: - Product rule: $$a^m \times a^n = a^{m+n}$$ (when multiplying same bases, add exponents) - Quotient rule: $$\frac{a^m}{a^n} = a^{m-n}$$ (when dividing same bases, subtract exponents) - Power rule: $$(a^m)^n = a^{m \times n}$$ (power of a power, multiply exponents) - Zero exponent rule: $$a^0 = 1$$ (any nonzero base to zero power is 1) - Negative exponent rule: $$a^{-n} = \frac{1}{a^n}$$ (negative exponent means reciprocal) - Power of a product: $$(ab)^n = a^n b^n$$ (distribute exponent to each factor) 4. These rules apply for any real number base $a \neq 0$ and integers $m,n$. 5. Using these rules helps simplify expressions and solve equations involving exponents easily. Final answer: The exponent rules are the product, quotient, power, zero, negative exponent, and power of a product rules as described above.