Bell WorkSimplify-2 – 4(-3) – 2(-2) – 2 2 3 2

Answer:-2 – 4(-3) – 2(-2) – 2= -4 – 4(-27) – 2(4) – 2= -4 +108 – 8 – 2= 94

2 32

Lesson 21:Product Rule for Exponents, Addition of Like Terms with Exponents

Product Rule for Exponents:

3 Means 3 x 3 x 3 x 3 x 3

3 3 Means (3 3) (3 3 3) or 3

3 3 means (3) (3 3 3 3) or 3

5

2 3 5

4 5

We see that when we multiply exponentials whose bases are the same, the exponent of the product is obtained by adding the exponents of the factors.

Example:

x x x = x p p = p

5 5 5 = 5 4 4 4 = 4

5 7 2 14 5 12 17

2 3 2 7 2 3 25 30

Product Rule for Exponents*: If m and n are real numbers and x ≠ 0, then x x = xm n m + n

Practice:Simplify:

x y x y2 2 5 3

Answer:x y7 5

Practice:Simplify:

x y m x y 2 3 5 3 2

Answer:x y m5 5 5

If any variable or constant is written without an exponent, it is understood to have an exponent of 1.

Practice:Simplify:

m p m x m x p

3 2 3 5

Answer:m x p6 4 6

Addition of like terms with exponents:When we multiply exponential expressions with like bases, we add the exponents. The task of adding like terms that contain exponents appears similar, but the rule is different.

When we add like terms that contain exponents, we do not add the exponents. Thus,

3x + 2x = 5xAnd does not equal 5x.

2 2 2

4

Addition and multiplication are often confused. When we add, we can only add like terms. We recall that letters stand for unspecified numbers and that the order of multiplication of real numbers can be changed.

Example:Simplify by adding like terms:

x yp + 2xy p + 3p x y – 7y xp2 5 2 5 5 2 2 5

Answer:4x yp – 5xy p2 5 2 5

Practice:Simplify by adding like terms:

2x y + 3yx + x y – x y – 4x y2 2 2 2 2 2 2

Answer:4x y – 3x y2 2 2

HW: Lesson 21 #1-30