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.

Learn the fundamental rules of exponents with this comprehensive guide, covering product, quotient, power rules, zero exponents, and negative exponents. Ideal for students in Grades 6-8, this guide explains how to simplify and manipulate expressions involving powers.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation