1. **Problem Statement:** Understand and apply the basic exponent rules with examples. 2. **Exponent Rules:** - Product Rule: $$a^m \times a^n = a^{m+n}$$ - Quotient Rule: $$\frac{a^m}{a^n} = a^{m-n}$$ - Power Rule: $$(a^m)^n = a^{m \times n}$$ - Zero Exponent Rule: $$a^0 = 1$$ (for $a \neq 0$) - Negative Exponent Rule: $$a^{-n} = \frac{1}{a^n}$$ 3. **Examples:** - Product Rule: $$2^3 \times 2^4 = 2^{3+4} = 2^7 = 128$$ - Quotient Rule: $$\frac{5^6}{5^2} = 5^{6-2} = 5^4 = 625$$ - Power Rule: $$(3^2)^3 = 3^{2 \times 3} = 3^6 = 729$$ - Zero Exponent Rule: $$7^0 = 1$$ - Negative Exponent Rule: $$4^{-2} = \frac{1}{4^2} = \frac{1}{16}$$ 4. **Explanation:** These rules help simplify expressions involving powers by combining or reducing exponents according to the operation (multiplication, division, or raising a power to another power). The zero exponent rule states any nonzero number raised to zero is 1, and negative exponents represent reciprocals. Final answer: The exponent rules are summarized and demonstrated above with clear examples.