>Lesson 58: Laws of Exponents (Product, Quotient, Power Rules)
Exponent rules help simplify expressions with powers. This lesson covers the product rule, quotient rule, and power rule.
Exponent Rules
- Product Rule: a^m × a^n = a^(m+n)
- Quotient Rule: a^m ÷ a^n = a^(m−n), a ≠0
- Power Rule: (a^m)^n = a^(m×n)
Examples
Example 1 (Product Rule): x^3 × x^5 = x^(3+5) = x^8
Example 2 (Quotient Rule): y^7 ÷ y^2 = y^(7−2) = y^5
Example 3 (Power Rule): (z^4)^3 = z^(4×3) = z^12
Example 4 (Combined): (x^2 × x^3)^4 ÷ x^5 = x^(2+3)^4 ÷ x^5 = x^20 ÷ x^5 = x^15
Practice Problems
- x^3 × x^6
- a^8 ÷ a^3
- (y^2)^5
- (m^3 × m^4)^2
- (p^6 ÷ p^2)^3