Lesson 1: 7-1 Multiplication Properties of Exponents
Duration of Days: 3
Lesson Objective
Multiply monomials using the properties of exponents.
Simplify expressions using the multiplication properties of exponents.
Why do we add the exponents when we multiply powers with the same base? How does writing the expression in expanded form justify the rule?
What is the critical difference between the expression x^2 • x^3 and the expression (x^2)^3? How do the two properties of exponents lead to different simplified answers?
What must be true about the bases of the terms before you can apply the Product of Powers Property (a^m • a^n = a^{m+n})? Can you simplify 2^5 • 3^4? Why or why not?
Monomial
Constant
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 multiply two powers that have the same base, ass their exponents. To find the power of a power, multiply exponents. To find the power of a product, find the power of each factor and multiply. Monomial expressions are simplifies when each base appears exactly once, there are no powers of powers, and all fractions are in simplest form.
Albert Einstein is perhaps the most well-known scientist of the 20th century. His formula E=mc^2, where E represents the energy, m is the mass of the material, and c is the speed of light, shows that if mass is accelerated enough, it could be converted into usable energy.
Students may simplify an expression using properties of exponents, not realizing that the simplification is incomplete because the fraction is not in the simplest form.
Logical learners. Give students an expression and challenge them to write ten different monomial expression that, when simplified, equal the given expression.
Beginning. Say key terms such as monomial, constant, exponent, base, and power, aloud, one at a time. Have students raise their hands if they have heard the term. Have them use a word or a phrase to tell something about the term. Use yes/no questions and prompts to help students complete a KWL Chart.
Intermediate. Have students work with a partner to complete the K section of the chart. Have partners seek clarification and discuss each term.
Advanced. After students complete the L section of the chart, have them work in groups to compare answers and add each other's information to their own charts.
Practice: Exercises 1 -20
Exercises 68-74