Chapter 8 sec. 1 What is a monomial and how do I multiply them?
A monomial is a number, a variable or a product (multiplication) of a number and one or more variables. • An expression involving the division of variables is NOT a monomial. • Monomials that are real numbers are called CONSTANTS
Identify Monomials • Expression Monomial Reason -5 ? Discuss/ fill in p + q ? x ? c/d ? abc2 / 5 ?
Product of Powers Review: 25 = (2)(2)(2)(2)(2) or 32 NOT (2)(5) = 10 small mistake = big difference in your work 25 Exponent base together = a power
Product of Powers Rule • When you multiply two powers that have the same base…….ADD THE EXPONENTS. Example: (5x7) (x6) STEPS 1. multiply the numbers 5x13 2. keep the variable 3. add the exponents
Example (4ab6)(-7a2b3) Steps: 1. multiply the numbers -28a3b92. keep the variables 3. add the exponents
Powers of Monomials • To find the power OF a power “mulitply the exponents.” It’s the same as ice cream and party only with exponents. Distribute the exponent to everything inside the parethesis. Example: (42)5 multiply the exponents 410
What do you do with a power raised to another power? ________________. [(32)3]2 = 312 or 531,441 (z8)3 = z24 Remember you are basically distributing the exponent to everything in the parenthesis.
Example: (4ab)2 = 42=a2b2 = 16a2b2 Example: (1/3xy4)2 [(-6y2)3] (12/32)(x2)(y8)(-63)(y6) 1/9x2y8(-216)y6
Practice (power to a power) (42)5 (xy)4 (-2xy)3
Practice Simplify: x (x4)(x6) (3y5z)2 (4/5 a2)2 (-2v3w4)3(-3vw3)2
Is the expression a monomial (y/n) 12 1/5 abc7 4x3 x/y2 a – 2b n