In this Grade 8 lesson from Big Ideas Math, Course 3, students learn the Quotient of Powers Property, which states that when dividing two powers with the same base, you subtract the exponents using the rule a^m divided by a^n equals a^(m-n). Students practice simplifying expressions involving numerical and variable bases, including multi-step problems that combine the Quotient of Powers Property with the Product of Powers Property, and apply the concept to a real-world population density problem.
Section 1
Quotient of Powers with Same Base
To divide two powers with the same base, we subtract the exponent in the denominator from the exponent in the numerator, and keep the same base.
In symbols:
This works for all integer exponents, including negative exponents.
Section 2
Simplifying Complex Expressions
When expressions contain both products and quotients of powers with the same base, apply the product property first to simplify the numerator and denominator separately, and then apply the quotient property:
When working with complex algebra fractions involving both multiplication and division of powers, follow a systematic two-step approach. First, clean up the top and bottom: use the product property to combine powers in the numerator and denominator separately by adding their exponents. Once you have a single power on top and a single power on the bottom, apply the quotient property by subtracting the exponents.
Section 3
Real-World Applications of the Quotient of Powers
Real-world problems often involve comparing quantities by division. When these quantities are expressed as powers with the same base, the Quotient of Powers Property can be used to simplify the comparison. The formula for comparison is often structured as:
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Section 1
Quotient of Powers with Same Base
To divide two powers with the same base, we subtract the exponent in the denominator from the exponent in the numerator, and keep the same base.
In symbols:
This works for all integer exponents, including negative exponents.
Section 2
Simplifying Complex Expressions
When expressions contain both products and quotients of powers with the same base, apply the product property first to simplify the numerator and denominator separately, and then apply the quotient property:
When working with complex algebra fractions involving both multiplication and division of powers, follow a systematic two-step approach. First, clean up the top and bottom: use the product property to combine powers in the numerator and denominator separately by adding their exponents. Once you have a single power on top and a single power on the bottom, apply the quotient property by subtracting the exponents.
Section 3
Real-World Applications of the Quotient of Powers
Real-world problems often involve comparing quantities by division. When these quantities are expressed as powers with the same base, the Quotient of Powers Property can be used to simplify the comparison. The formula for comparison is often structured as:
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter