1. The problem: Understand and explain the exponent rules. 2. Exponent rules are formulas that help us simplify expressions involving powers. 3. Important rules include: - 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: $a^0 = 1$ (if $a \neq 0$) - Negative exponent: $a^{-n} = \frac{1}{a^n}$ 4. Explanation: - When multiplying powers with the same base, add the exponents. - When dividing powers with the same base, subtract the exponents. - When raising a power to another power, multiply the exponents. - Any nonzero number raised to zero is 1. - A negative exponent means take the reciprocal of the base raised to the positive exponent. 5. Example: Simplify $2^3 \times 2^4$ - Using product rule: $2^{3+4} = 2^7 = 128$ 6. Example: Simplify $\frac{5^6}{5^2}$ - Using quotient rule: $5^{6-2} = 5^4 = 625$ 7. Example: Simplify $(3^2)^4$ - Using power rule: $3^{2 \times 4} = 3^8 = 6561$ 8. Example: Simplify $7^0$ - Using zero exponent rule: $7^0 = 1$ 9. Example: Simplify $4^{-3}$ - Using negative exponent rule: $4^{-3} = \frac{1}{4^3} = \frac{1}{64}$ These rules help simplify and solve many algebra problems involving exponents.