5.1 - Monomials

Section 5.1 – Monomials

Date: ____/_____/_______

Definition: A monomial is an expression that is a #, a variable or the product of a # and one or more variables. Monomials cannot contain variables in the denominators nor variables with negative exponents, nor variables under radicals. Ex1 Tell whether each expression is a monomial. If not explain. 1) 2) 3) 4) 5)

HW Pg 226 Honors: 18 – 58 (evens). Regular: 2-28 (evens), 34, 36, 44, 46, 50, 52, 54

St1 Same directions 1)

5x x+8 x-1 x 25

1 n4

2) x2 3) x – 5

Definition: Constants are monomial that contain NO VARIABLE. Example: 25, 3, -45, 1/3, 2/3, …

Rule of Exponents 1) a−n =

1 n

m n m + n 2) a ⋅a=a

am 3) =am−n an a Quotient

Negative Exponents

mn m ⋅n 4) (a )= a

Product of Powers

m m 5) (a ⋅b )m= a ⋅b Power of a Product

 an an 6)   = n b b

Quotient of Powers

Ex2 Simplify expression with powers. Name the properties.

St2 Same directions.

1) (2a3)6 2)

−3x4    y  −3

 a 3)    4

1)

(3b )

2)

−2x6    yz 

3 3

 5 −2 3)    m

Power of a Power

Product of

Ex3 Simplify expression with several properties −2x3n 4  2n 3  = x y 

St3 Same directions

−3ab 2n 3  2n −2  = b c 

Scientific Notation: Is used to express very large numbers or very small numbers.

ax10n where 1≤ a < 10 Ex4 Express each number in scientific notation.

St 4 Same directions

a) 6,380,000 =

c) 4,560,000 =

b) 0.00047 =

d) 0.000092 =

Ex5 Evaluate. Express result in scientific notation a) St a)

(4x10 5)(2x10 7) = (2.7x10 -2)(3x10 6) =

Ex6 Biology. There are about 5x106 red blood cells in one milliliter of blood. A certain blood sample contains 8.32x106 red blood cells. About how many milliliters of blood are there in the sample.

Answer__________________________