In this Grade 7 lesson from Big Ideas Math Course 2 Accelerated, students learn the Quotient of Powers Property, which states that dividing two powers with the same base is equivalent to subtracting their exponents (a^m ÷ a^n = a^(m−n)). Through hands-on activities, students practice simplifying expressions like 2^6 ÷ 2^4 by applying this rule to bases that include integers, decimals, and variables. The lesson builds toward the 8.EE.1 standard by helping students recognize patterns in repeated multiplication and generalize a reliable method for simplifying quotients of powers.
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
Multiple Quotients in Single Expressions
When an expression contains multiple quotients with the same base, apply the quotient property to each quotient separately:
Section 3
Dividing Monomials
To divide monomials, divide the coefficients and then divide variables with the same base by subtracting their exponents. For variables with the same base, the Quotient of Powers Property is applied.
Section 4
Application: Population Density
Population density is calculated by dividing the total population by the land area.
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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
Multiple Quotients in Single Expressions
When an expression contains multiple quotients with the same base, apply the quotient property to each quotient separately:
Section 3
Dividing Monomials
To divide monomials, divide the coefficients and then divide variables with the same base by subtracting their exponents. For variables with the same base, the Quotient of Powers Property is applied.
Section 4
Application: Population Density
Population density is calculated by dividing the total population by the land area.
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter