Multiple Quotients in Single Expressions
Multiple Quotients in Single Expressions is a Grade 7 math skill in Big Ideas Math Advanced 2, Chapter 10: Exponents and Scientific Notation, where students simplify expressions that contain two or more division operations involving powers, applying the quotient of powers rule (subtract exponents) to each quotient and combining results. This extends exponent fluency to multi-term expressions.
Key Concepts
When an expression contains multiple quotients with the same base, apply the quotient property to each quotient separately: $\frac{a^m}{a^n} \cdot \frac{a^p}{a^q} = a^{m n} \cdot a^{p q} = a^{(m n)+(p q)}$.
Common Questions
What is the quotient of powers rule?
When dividing two powers with the same base, subtract the exponents: a^m / a^n = a^(m-n). For example, x^7 / x^3 = x^(7-3) = x^4.
How do you simplify an expression with multiple quotients of powers?
Apply the quotient rule to each pair of like-base powers independently, then multiply or simplify the resulting powers. Keep track of each base separately.
What happens when the exponent in the denominator is larger than in the numerator?
The result has a negative exponent, which means the factor belongs in the denominator. For example, x^2 / x^5 = x^(2-5) = x^-3 = 1/x^3.
What is Big Ideas Math Advanced 2 Chapter 10 about?
Chapter 10 covers Exponents and Scientific Notation, including the product, quotient, and power of powers rules, zero and negative exponents, and scientific notation operations.