2. Exponents For all real numbers x and all positive integers m, xm = x x x … x, m factors Evaluate: 1.2 8 2. 5 3 3. 3 4 4. 6 1 Answers: 1. 256 2. 125 3. 814. 6

3. PRODUCT OF POWERS Product of Powers Property For all real numbers x and all integers m and n, xm xn = xm+n KEEP the BASE then ADD the EXPONENTS!

4. Example: Simplify the following: 1.2 5 2 4 2.8 8 3 3.y 2 y 5 4.5 m 5 p 5.z 6 z 3 6.a z a 3 25 + 4 = 29 = 512 81 + 3 = 84 = 4096 y2 + 5 = y7 5m + p z6 + 3 = z9 az + 3

5. Multiplying Monomials DefinitionMonomial - A monomial is an algebraic expression that is either a constant, a variable, or a product of a constant and one or more variables. The constant is called coefficient. To simplify a product of monomials, 1.Multiply the coefficients. 2.Add the exponents of the same variables.

6. Examples: Simplify. 1.(5x)(-30x 2 ) 2.(-4a 2 b)(-ac 2 )(3b 2 c 2 ) 3. (3m 2 )(60mp 2 ) -150x3 12a3b3c4 180m3p2

7. Simplify. 3.(8xz)(-10y)(-2yz 2 ) 4.(3xy 2 )(-5x 2 y)(y 3 z) 5.(-2c 2 )(3x 3 ) 6. (3x a y b z c )(-y n z m ) 160xy2z3 -15x3y6z -6c2x3 -3xa yb + nzc + m

8. Geometry Connection The volume, V, of a right rectangular prism can be found by using the formula V = lwh, where l is the length, w is the width and h is the height. Suppose that the prism has a length of 2xy, a width of 3xy, and a height of 6xyz. Find the volume. Solution: V = lwh = (2xy)(3xy)(6xyz) V= 36x 3 y 3 z

9. The area, A, of a trapezoid can be found by using the formula A = ½ h(b 1 + b 2 ), where b 1 is one base and b 2 is the other base, and h is the height. Suppose that a trapezoid has a base of 5x, another base of 9x, and a height of 8xy. Find the area. Solution: A = ½ h(b 1 + b 2 ), = ½ (8xy)(5x + 9x) = ½ (8xy)(14x) A= 56x 2 y

10. Do these… 1.The volume, V, of a right rectangular prism can be found by using the formula V = lwh, where l is the length, w is the width and h is the height. Suppose that the prism has a length of 3rt, a width of 5rt, and a height of 2rty. Find the volume. Answer: 30r 3 t 3 y 2. The area, A, of a triangle can be found using the formula A = ½ bh, where b is the base and h is the height of the triangle. Find the area of a triangle with base 10x 2 y and height 7x 3 y 5. Answer: 35x 5 y 6

11. Time to do your work…. Get a sheet of paper and do the assigned CLASSWORK! WORK SILENTLY!!!!