SWBAT… multiply monomials Thurs, 2/8 Agenda 1. WU (5 min) 2. Practice problems (10 min) 3. Review HW#1 (10 min) 4. Lesson on multiplying monomials (3 slides & lots of ex) Warm-Up:

Laws of Exponents

Product of Powers (3) Words: To multiply two powers that have the same base, add their exponents. Symbols: For any real number x and any integers m and n, x m x n = x m + n Examples (x 3 )(x 4 ) = x 3+4 = x 7 OR (x 3 )(x 4 ) = (xxx)(xxxx) = xxxxxxx = x 7 Open Ended: Create a problem that satisfies this property!

Examples

Power of a Power (4) Words: To raise a power to a power, multiply the exponents. Symbols: For any real number x and any integers m and n, (x m ) n = x m ∙ n Examples: (x 2 ) 4 = x 2∙4 = x 8 OR (x 2 ) 4 = (x 2 )(x 2 )(x 2 )(x 2 ) = (xx)(xx)(xx)(xx) = x 8 (b 3 ) 5 = b 3∙5 = b 15 Open Ended: Create a problem that satisfies this property!

Examples

Power of a Product (5) Words: If you have a product inside parentheses, and a power on the parentheses, then the power goes on each number and variable inside (both the numerator and the denominator) Symbols: For any real number x and any integer m, (xy) m = x m y m Examples (xy) 3 = x 3 y 3 OR (xy)(xy)(xy) = (xxx)(yyy) = x 3 y 3

Examples

Simplifying Monomials: Warm-Up:

Answers

Using formulas and correct units The volume of a cone can be represented by the formula V = πr 2 h. Find the volume if the radius is 3x inches and the height is 5x 2 inches. Leave your answer in terms of π.

When working with exponents, you're dealing with multiplication. Since order doesn't matter for multiplication, you will often find that you and a friend (or you and the teacher) have worked out the same problem with completely different steps, but have gotten the same answer in the end. This is to be expected. As long as you do each step correctly, you should get the correct answers. Don't worry if your solution doesn't look anything like your friend's; as long as you both got the right answer, you probably both did it "the right way".