8.1

1. 8.1 Multiplying Monomials and Raising Monomials to Powers

2. Vocabulary • Monomials - 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.

3. 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.

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

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

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

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

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

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

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

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

12. 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 = am•bm

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

14. Practice Problems Page 413 Problems: 15-40