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Monomials Multiplying Monomials and Raising Monomials to Powers

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Vocabulary Monomials - a number, a variable, or a product of a number and one or more variables 4x, 20x 2 yw 3, -3, a 2 b 3, and 3yz are all monomials. Constant – a monomial that is a number without a variable. Base – In an expression of the form x n, the base is x. Exponent – In an expression of the form x n, the exponent is n.

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Writing - Using Exponents Rewrite the following expressions using exponents: The variables, x and y, represent the bases. The number of times each base is multiplied by itself will be the value of the exponent.

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Writing Expressions without Exponents Write out each expression without exponents (as multiplication): or

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Simplify the following expression: (5a 2 )(a 5 ) Step 1: Write out the expressions in expanded form. Step 2: Rewrite using exponents. Product of Powers There are two monomials. Underline them. What operation is between the two monomials? Multiplication!

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For any number a, and all integers m and n, a m a n = a m+n. Product of Powers Rule

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If the monomials have coefficients, multiply those, but still add the powers. Multiplying Monomials

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These monomials have a mixture of different variables. Only add powers of like variables. Multiplying Monomials

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Simplify the following: ( x 3 ) 4 Note: 3 x 4 = 12. Power of Powers The monomial is the term inside the parentheses. Step 1: Write out the expression in expanded form. Step 2: Simplify, writing as a power.

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Power of Powers Rule For any number, a, and all integers m and n,

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Monomials to Powers If the monomial inside the parentheses has a coefficient, raise the coefficient to the power, but still multiply the variable powers.

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Monomials to Powers (Power of a Product) If the monomial inside the parentheses has more than one variable, raise each variable to the outside power using the power of a power rule. (ab) m = a m b m

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Monomials to Powers (Power of a Product) Simplify each expression:

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What about dividing monomials?

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1.Be able to divide polynomials 2.Be able to simplify expressions involving powers of monomials by applying the division properties of powers.

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Simplify: Step 1: Rewrite the expression in expanded form Step 2: Simplify. For all real numbers a, and integers m and n: Remember: A number divided by itself is 1.

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Simplify: Step 1: Write the exponent in expanded form. Step 2: Multiply and simplify. For all real numbers a and b, and integer m:

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Apply quotient of powers. Apply power of a quotient. Apply quotient of powers Apply power of a quotient Simplify Apply power of a power

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1. 2. THINK! x 3-3 = x 0 = 1

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