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8.1 MONOMIAL Multiplying Monomials and Raising Monomials to Powers VOCABULARY Let's start with what we know... Constant – a number by itself Coefficient – a number used to multiply a variable (in front of the variable or variable combinations) Term – a number, variable, or combination of numbers and variables. VOCABULARY TERMS ARE MONOMIALS!!! Monomials – a number, a variable, or a product of a number and one or more variables EXAMPLES: Base – In an expression of the form xn, the base is x Exponent – In an expression of the form xn, the exponent is n x 3 x 3 EXPONENTS AND FORMS What does this mean? That's three 2's all multiplied together! Exponential form Expanded form In Algebra, we work with variables like x. What if there is a coefficient? WRITING IN EXPONENTIAL FORM Rewrite the following expressions using exponents: x x x x y y a a a b b b b c c d e e WRITING IN EXPANDED FORM... Rewrite the following expressions WITHOUT using exponents: LET'S LOOK AT OPERATIONS... Can we add these? Can we multiply them? Write out what each one means and see what happens... Example 1: Example 2: PRODUCT OF POWERS RULE Try These: WHEN CAN'T I USE THIS? This is addition--not multiplication-and they are NOT like terms! The bases don't match! There is nothing we can do with either of these! MULTIPLYING MONOMIALS WITH COEFFICIENTS Multiply the coefficients but still add the powers. Try These: MULTIPLYING MONOMIALS WITH DIFFERENT VARIABLES Only add powers of like variables. Example 3: You Try: MULTIPLYING MONOMIALS WITH DIFFERENT VARIABLES Try These: POWER TO A POWER RULE Simplify the following: Step 1: Write out the expression in expanded form. Step 2: Simplify, writing as a power. Example 4: POWER TO A POWER RULE Try These: POWER TO A POWER WITH COEFFICIENT Raise the coefficient to the power, but still multiply the variable powers. Try These: POWER TO A POWER WITH MORE THAN ONE VARIABLE Raise each variable to the outside power using the power to a power rule. (ab)m = am bm Example 5: You Try: POWER TO A POWER WITH MORE THAN ONE VARIABLE Example 6: POWER TO A POWER WITH MORE THAN ONE VARIABLE Try These: