The rules of exponents, also known as the laws of exponents, describe how to simplify and manipulate expressions involving powers. Here are the key rules:

1. Product of Powers Rule: $a^m \times a^n = a^{m+n}$ When multiplying two exponents with the same base, you add the exponents.

2. Quotient of Powers Rule: $\frac{a^m}{a^n} = a^{m-n}$ When dividing two exponents with the same base, you subtract the exponents.

3. Power of a Power Rule: $(a^m)^n = a^{m \times n}$ When raising a power to another power, you multiply the exponents.

4. Power of a Product Rule: $(ab)^n = a^n \times b^n$ When raising a product to an exponent, apply the exponent to each factor in the product.

5. Power of a Quotient Rule: $\left(\frac{a}{b}\right)^n = \frac{a^n}{b^n}$ When raising a quotient to an exponent, apply the exponent to both the numerator and denominator.

6. Zero Exponent Rule: $a^0 = 1 \quad \text{(for } a \neq 0\text{)}$ Any non-zero number raised to the power of zero is equal to 1.

7. Negative Exponent Rule: $a^{-n} = \frac{1}{a^n}$ A negative exponent indicates the reciprocal of the base raised to the positive exponent.

---

Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:

1. How do you simplify expressions using the power of a power rule?
2. What happens when you apply the power of a quotient rule to a fraction?
3. Can you explain why any number raised to the power of zero equals 1?
4. How do negative exponents affect the position of a term in a fraction?
5. How do the rules of exponents apply to expressions with variables?

Tip: Always pay attention to the base when applying exponent rules; the rules only work when the base is the same.