Overview
This lecture explains how to apply the order of operations (PEMDAS) with exponents, negative signs, and parentheses.
Order of Operations (PEMDAS)
- PEMDAS stands for Parentheses, Exponents, Multiplication, Division, Addition, and Subtraction.
- Always solve expressions in this order to get the correct result.
Working with Squares and Negatives
- ( 3^2 ) means 3 × 3, which equals 9.
- ( -3^2 ) means the negative is applied after squaring: 3 × 3 = 9, then -1 × 9 = -9.
- ( (-3)^2 ) means square negative 3: (-3) × (-3) = 9, since two negatives make a positive.
Negative Exponents
- ( 3^{-2} ) means take the reciprocal of 3 squared: ( 1/(3^2) = 1/9 ).
- ( (-3)^{-2} ) means take the reciprocal of negative 3 squared: ( 1/((-3)^2) = 1/9 ).
Key Terms & Definitions
- PEMDAS — order to solve expressions: Parentheses, Exponents, Multiplication, Division, Addition, Subtraction.
- Exponent — shows how many times to multiply a number by itself.
- Negative exponent — means take the reciprocal of the base number raised to the positive exponent.
Action Items / Next Steps
- Practice evaluating expressions involving exponents, negatives, and parentheses using PEMDAS.
- Review homework problems on order of operations and exponent rules.