Application: Product and Quotient Rules with Negative Exponents
Grade 7 students in Big Ideas Math Advanced 2 (Chapter 10: Exponents and Scientific Notation) apply product and quotient rules to expressions involving zero and negative exponents. The product rule adds exponents and the quotient rule subtracts exponents regardless of sign.
Key Concepts
When simplifying expressions with like bases and zero or negative exponents: Product Rule: $a^m \cdot a^n = a^{m+n}$ Quotient Rule: $\frac{a^m}{a^n} = a^{m n}$ These rules apply regardless of whether exponents are positive, negative, or zero.
Common Questions
How do you apply the product rule with negative exponents?
Add the exponents: x^(-3) x x^5 = x^(-3+5) = x^2. The product rule a^m times a^n = a^(m+n) works even with negative exponents.
How do you apply the quotient rule with negative exponents?
Subtract exponents: y^2 divided by y^(-4) = y^(2-(-4)) = y^(2+4) = y^6. Subtracting a negative adds.
How do you simplify an expression with zero exponents?
Any nonzero base to the zero power equals 1: z^0 = 1. In products: z^0 times z^(-2) times z^3 = z^(0-2+3) = z^1 = z.
What chapter in Big Ideas Math Advanced 2 covers product and quotient rules with negative exponents?
Chapter 10: Exponents and Scientific Notation in Big Ideas Math Advanced 2 (Grade 7) covers product and quotient rules with negative exponents.
Should final answers be written with positive exponents?
Typically yes. Convert negative exponents: a^(-n) = 1/a^n. For example, x^(-3) = 1/x^3.