2. Multiplying and Dividing Monomials 4.3

3. Monomial: An expression that is either a: (1) numeral or constant, ex : 5 (2)a v ariable, ex: x (3)or a product of numerals and variables ex: 5x (4)variables with whole number exponents. Ex: x² If the monomial is a numeral, it is called a constant. Excludes: “+”, “-”, and if exponent is negative or a fraction. 4x 3 x 3 + 4 -8 2x 2 y

4. x 3 means: x x x x 2 means: x x x 3 x 2 means (x x x) (x x) x5x5 Multiplying Powers with the same base: X m x n = x m+n

5. Simplify. Express using exponents. 8 4 8 3 8 4+3 = 8 7

6. Simplify. Express using exponents. y y 2 y 6 y 1+2+6 = y 9

7. Multiply 2 monomials using “properties” (3x 4x) = (3 4)(x x) = 12x 2 (Associative and Commutative) Group the numbers together and then group the same variables together (3x 2 )(-x) = (3x 2 )(-1x) = (3 - 1)(x 2 x) = -3x 3 (-7x 2 y 5 )(4xy 3 ) (-7 4)(x 2 x)(y 5 y 3 ) -28x 3 y 8

8. Simplify. Express using exponents. (mn 2 ) (m 4 n 6 ) m 1+4 n 2+6 = m 5 n 8

9. Simplify. Express using exponents. (7x2y4) (3x4y6)(7x2y4) (3x4y6) x 2+4 y 4+6 = 21x 6 y 10 21

10. Simplify. Express using exponents. (9x3y2) (6x5y3)(9x3y2) (6x5y3) 54x 8 y 5

11. Multiply: (-3y 3 )(4xy 5 ) = -12xy 8

12. Dividing Powers with the same base: X m ÷ x n = x m-n Dividing Powers with the Same Base

13. Simplify. Express using exponents.

15. Divide monomials using properties: Group the numbers together and either divide or reduce and then group the like bases together.

16. Simplify. Express using exponents.

17. 4

19. Divide monomials using properties:

20. Simplify:

23. Homework CA Math Page 150 (20-60) even