1. The problem: Understand the basic rules of exponents. 2. Rule 1: Product of powers with the same base $$a^m \times a^n = a^{m+n}$$ This means when multiplying powers with the same base, add the exponents. 3. Rule 2: Quotient of powers with the same base $$\frac{a^m}{a^n} = a^{m-n}$$ When dividing powers with the same base, subtract the exponents. 4. Rule 3: Power of a power $$(a^m)^n = a^{m \times n}$$ When raising a power to another power, multiply the exponents. 5. Rule 4: Power of a product $$(ab)^n = a^n b^n$$ Distribute the exponent to each factor inside the parentheses. 6. Rule 5: Power of a quotient $$\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}$$ Distribute the exponent to numerator and denominator. 7. Rule 6: Zero exponent $$a^0 = 1$$ Any nonzero number raised to the zero power equals 1. 8. Rule 7: Negative exponent $$a^{-n} = \frac{1}{a^n}$$ A negative exponent means take the reciprocal of the positive exponent. These rules help simplify expressions involving exponents and are fundamental in algebra.