1. Chapter 8.1

2.  Lesson Objective: NCSCOS 1.01 – Write the equivalent forms of algebraic expressions to solve problems  Students will know how to apply the laws of exponents when multiplying monomials.

3.  Example 1-  Simplify: x 2 * x 3  Remember: x 2 = x * x which can also be written as xx  x 2 = x * x and x 3 = x * x * x  Therefore x 2 * x 3 = (x*x)*(x*x*x) = xx * xxx = xxxxx  There are 5 x’s in the answer  Therefore x 2 * x 3 = x 5  Rule: When multiplying monomials you must add the exponents together. X m * x n = x m+n

4. 1. 3 3 * 3 4 2. x 3 * x 4 3. x 5 (x 3 ) 4. x 7 (x -2 )

5. 1. 3 3 * 3 4 2. x 3 * x 4 3. x 5 (x 3 ) 4. x 7 (x -2 ) 3737 x7x7 x8x8 x5x5

6.  Example 2-  Simplify (2x 3 )(3x 4 )  Multiply the numbers together first: 2 * 3 = 6  Multiply the variables together second: x 3 * x 4 = x 7  Put the numbers and letters back together for your answer: 6x 7  Rule: When multiplying monomials you multiply the numbers and letter separately

7. 1. 3x 3 * 4x 2 2. 5x 4 (2x 3 ) 3. -2x 2 (4x) 4. -7x(-3x 3 )

8. 1. 3x 3 * 4x 2 2. 5x 4 (2x 3 ) 3. -2x 2 (4x) 4. -7x(-3x 3 ) 12x 5 10x 7 -8x 3 21x 4

9.  Example 3-  Simplify (-2x 2 y 3 )(3x 5 y 2 )  Multiply the numbers together first: –2 * 3 = -6  Multiply the x’s separately: x 2 * x 5 = x 7  Multiply the y’s separately: y 3 * y 2 = y 5

11. 1. 3x 3 y 2 * 4x 2 y 2 2. 5x 4 y 3 (2x 3 y 4 ) 3. -2x 2 y 2 (4xy) 4. -7xy(-3x 3 y 3 ) 12x 5 y 4 10x 7 y 7 -8x 3 y 3 21x 4 y 4

12.  Example 4  Simplify (x 3 ) 2  Remember, (x 3 ) 2 = (x 3 ) * (x 3 ) = xxx * xxx  Therefore (x 3 ) 2 = x 6  Rule: When a monomial with an exponent is then raised to an exponent you multiply the exponents together. (X m ) n = x m*n  You can always write out x 3 twice and add the exponents

13. 1. (x 2 ) 3 2. (x 4 ) 4 3. (x 3 ) 7

14. 1. (x 2 ) 3 2. (x 4 ) 4 3. (x 3 ) 7 x6x6 x 16 x 21

15.  Example 5  Simplify: 2x 2 (3x 3 ) 2  Remember order of operations, exponents come before multiplication!  Also, any number squared means to multiply it by itself  Therefore: 2x 2 (3x 3 )(3x 3 )  Multiply the numbers: 2 * 3 * 3 = 18  Multiply the variables: x 2 * x 3 * x 3 = x 8  Put the numbers and letters back together: 18x 8

16. 1. 2x 2 (3x 3 ) 2 2. (4x 3 ) 2 (2x 5 ) 3. (3x 4 ) 3 (2x 3 ) 2

17. 1. 2x 2 (3x 3 ) 2 2. (4x 3 ) 2 (2x 5 ) 3. (3x 4 ) 3 (2x 3 ) 2 18x 8 108x 18 32x 11

18. 1. x 2 * x 3 2. 3x(2x 3 ) 3. -2x 3 (4x 4 ) 4. (x 4 ) 3 5. 2x 3 (3x 4 ) 2

19. 1. x 2 * x 3 2. 3x(2x 3 ) 3. -2x 3 (4x 4 ) 4. (x 4 ) 3 5. 2x 3 (3x 4 ) 2 x5x5 6x 4 x 12 -8x 7 18x 11