MONOMIALS!!

Today’s Objectives:

identify and write monomialsapply properties of powers and properties of exponent to monomials

Observe the following expressions…

€

9€

x

€

3p

€

−20y

€

3c 5

€

4xy 3

€

13 x

3y 4

€

5ab

€

−x7

What were your categories?

Definition of a Monomial

A monomial is:– A number– A variable– The product of a number and a variable

A monomial cannot contain:– Variables in the denominator– Variables with exponents that are negative– Variable under radicals

Some important concepts…

Constants– Monomials that contain no variables

Coefficient– Numerical factor of a monomial

Degree– The sum of the exponents on the variables

Power– Expression of the form xn

Properties of Exponents

€

x a ⋅ x b = x a+b

€

x a

x b= x a−b

Operations

Adding Subtracting

€

4x 2y + 7x 2y

€

3ab2 + 6a2b

€

8a3c 4 −12a3c 4€

−3a2b2 + 6a2b

Operations

Multiplying Dividing

€

(−7x 2y)(−3xy 3z5)

€

−35a4b3c 7

7ab5c 4

Properties of Powers

€

(x a )b = x ab

€

(xy)a = x ay a

€

xy ⎛ ⎝ ⎜

⎞ ⎠ ⎟a

= x a

y a ⎛ ⎝ ⎜

⎞ ⎠ ⎟

€

8x 5y 5

(x 2y)2

⎡ ⎣ ⎢

⎤ ⎦ ⎥2

Before you leave…

For each property discussed today form one example to represent. Label the property being presented.– Product of Powers– Quotient of Powers– Power of a Power– Power of a Product– Power of a Quotient

€

(−2a5)2

8b2a

⎡ ⎣ ⎢

⎤ ⎦ ⎥3

€

(3a)2(2a2b)b

⎡ ⎣ ⎢

⎤ ⎦ ⎥2

€

2b5(b3a2)a2b

⎡ ⎣ ⎢

⎤ ⎦ ⎥2

Also, choose one of the following…

Simplify using properties of exponents and properties of powers. For each step state the operation used.

WITHOUT a calculator

101000

10010

(1010×10100)10

1000

10/1010

1010×10100×100(1010)10

Based on our knowledge of exponents, place the following in ascending order…

(10/100)10

110010/1010