To multiply monomials, we add the exponents of the same bases. This follows the product of powers rule, which states that for any real numbers b and positive integers m and n, bm * bn = bm+n. To multiply monomial expressions, we use the commutative and associative properties of multiplication to group like bases together before adding their exponents.

2. What is 36? 36 = 3 * 3 * 3 * 3 * 3 * 3 How else can we look at 36? 36 = (3 * 3) * (3 * 3 * 3 * 3) =32 * 34 36 = (3 * 3 * 3) * (3 * 3 * 3) = 33 * 33 36 = (3 * 3 * 3 * 3 * 3) * 3 = 35 = 31 What is the pattern?

3. What is a monomial? A monomial is either a constant, a variable, or a product of a constant and one or more variables: Constants: 1 -3 ⅓ 5.2 Variables: x k a Product: 4x3 -5xy πr2 (⅛)x NOT a monomial: a2 + b2

4. Multiplying Monomials The monomials a3 and a4 have the same base a but different exponents, 3 and 4. To multiply a3 and a4, we add the 3 and the 4: a3 * a4 = (a*a*a)*(a*a*a*a) = a3+4 = a7

5. Product of Powers For all real numbers b and all positive integers m and n, bm * bn = bm+n

6. Try some: r7 * r c2 * d2 x4 * y6 a2 * a3

7. What about (-3c2d)(7cd3)? Use the commutative and associative properties of multiplication to group the constant coefficients together and the like bases together: (-3*7)*(c2*c)(d*d3) -21c3d4

8. Try some: (-5x2y)(-xz3) x2y(x2y2) Evaluate for x = -3 and y = -1

9. Try some: (3a5b4c)(-2b3c8) (xy3)(x2y3) Evaluate for x = -5 and y = 2

10. Turn to page 202 Do 1-12