Lesson 2: 7-2 Division Properties of Exponents
Duration of Days: 1.5
Lesson Objective
Divide monomials using the properties of exponents.
Simplify expressions containing negative and zero exponents.
How does the process of canceling out common factors in the expanded form of a division problem (like {x^5}/{x^3}) lead directly to the rule of subtracting the exponents? What does the remaining exponent actually represent?
When you use the Quotient of Powers Property on an expression where the numerator and denominator are equal (like {y^4}/{y^4}), the resulting exponent is zero. What is the value of the original fraction ({y^4}/{y^4}), and how does this result prove that any non-zero base raised to the power of zero must equal 1?
If you apply the Quotient of Powers Property to {a^3}/{a^7}, the resulting exponent is negative. How do you interpret the meaning of a^{-4}, and why does the definition of a negative exponent 1/{a^4} ensure the answer is consistent with the expanded form of the original fraction?
Order of magnitude
A.SSE.2 Use the structure of an expression to identify ways to rewrite it.
F.IF.8b Use the properties of exponents to interpret expressions for exponential functions.
See below
To divide two powers that have the same base, subtract exponents. To find the power of a quotient, find the power of the numerator and the power of the denominator. A nonzero number raised to a negative integer power is the reciprocal of the same number with the opposite power. A fraction that has negative exponent can be rewritten as its reciprocal with a positive power.
Darin has $123,456 in his savings account. Tabo has $156 in his savings account Determine the order of magnitude of Darin's account and Tabo's account. How many orders of magnitude as great is Darin's account as Tabo's account?
Remind students to also find the powers of the constant terms of the monomials.
If students have difficulty relating the key concepts in this lesson to expressions, then have students make flash cards to illustrate each key concept, Write an expression that is an example of a key concept on the board, Tell students to show their card that correlates to the example. Then ask a student to describe the process.
Practice: Exercises 1 -18
Exercises 66-72