Overview
This lecture reviews the main exponent laws, explaining how to simplify expressions using rules for multiplying, dividing, and raising exponents.
Product of Powers
- When multiplying powers with the same base, add the exponents: ( m^a \times m^b = m^{a+b} ).
- Example: ( m^4 \times m^{-3} = m^{4+(-3)} = m^1 = m ).
Quotient of Powers
- When dividing powers with the same base, subtract the exponents: ( m^a / m^b = m^{a-b} ).
- Example: ( m^7 / m^{-2} = m^{7-(-2)} = m^9 ).
Power of a Power
- When raising a power to another exponent, multiply the exponents: ( (m^a)^b = m^{a \times b} ).
- Example: ( (m^3)^4 = m^{3 \times 4} = m^{12} ).
Power of a Product
- When raising a product to an exponent, apply the exponent to each factor: ( (ab)^m = a^m b^m ).
- Example: ( (xy)^3 = x^3 y^3 ).
Power of a Quotient
- When raising a quotient to an exponent, apply the exponent to both numerator and denominator: ( (a/b)^m = a^m / b^m ), with ( b \neq 0 ).
- Example: ( (x/y)^2 = x^2 / y^2 ).
Key Terms & Definitions
- Exponent — A number that shows how many times the base is multiplied by itself.
- Base — The number being raised to a power.
- Product of Powers — Multiply same bases, add exponents.
- Quotient of Powers — Divide same bases, subtract exponents.
- Power of a Power — Multiply exponents when raising a power to a power.
- Power of a Product — Raise each factor in a product to the exponent.
- Power of a Quotient — Raise numerator and denominator to the exponent.
Action Items / Next Steps
- Practice problems using each exponent law.
- Review any homework assigned on exponent operations.