8.1Multiplying Monomials and Raising Monomials to Powers

VocabularyMonomials - a number, a variable, or a product of a number and one or more variables 4x, 20x2yw3, -3, a2b3, and 3yz are all monomials.Constant a monomial that is a number without a variable.Base In an expression of the form xn, the base is x.Exponent In an expression of the form xn, the exponent is n.

Writing - Using ExponentsRewrite 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.

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

Simplify the following expression: (5a2)(a5)Step 1: Write out the expressions in expanded form.Step 2: Rewrite using exponents. Product of PowersThere are two monomials. Underline them.What operation is between the two monomials?Multiplication!

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

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

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

Simplify the following: ( x3 ) 4 Note: 3 x 4 = 12.Power of PowersThe monomial is the term inside the parentheses. Write out the expression in expanded form.Simplify, writing as a power.

Power of Powers Rule

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

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 = ambm

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

Practice ProblemsPage 413Problems: 15-40

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