february 24, 2015
TRANSCRIPT
Monomials
Multiplying & Dividing Monomials
and Raising Monomials to Powers
Today:
Vocabulary
Monomials - a number, a variable, or a product of a number and one or more variables
4x, 20x2yw3, -3, a2b3, and 3yz are all monomials. Constant – a monomial that is a number without a variable. Base – In an expression of the form xn, the base is x. Exponent – In an expression of the form xn, the exponent is
n.
Writing Expressions Using Exponents
Write the expression with exponents
(as multiplication):
8a3b38 ● a ● a ● a ● b ● b ● b =Could the above expression be
written as a power of a product? ( )x
x x x x y y y y
xy xy xy xy xy 4or
Simplify the following expression: (5a2)(a5)
Step 1: Write out the expressions in expanded form.
Step 2: Rewrite using exponents.
Product Rule
5a2 a5 5 a a a a a a a
How many terms are there?
What operation is being performed? Multiplication!
5a2 a5 5 a
7 5a
7
Multiplying Monomials: The Product Rule
4) 3k5mn
4 7k3m
3n
3
5) 12 x2y
3 2xy2 24x
3y
5
21k8m
4n
7
If the monomials have coefficients, multiply those, but still add powers of common bases.
If the monomial inside the parentheses has more than one variable, raise each variable to the outside power using the power of a power rule.
(ab)m = am•bm
(9xy)2 = (-5x)2 = -(5x)2 =
Simplify the following: ( x3 ) 4
Note: 3 x 4 = 12
The monomial is the term inside the parentheses.
1. Multiply the exponents, write the simplified monomial
x3
4
x12
For any number, a, and all integers m and n,
am n
amn .
1) b9
10
b90
2) c3
3
c9
1) 2b9
3
8b27
2) 5c3
3
125c9
3) 7w12
2
49w24
If the monomial inside the parentheses has a coefficient, raise the coefficient to the power, but still
multiply the variable powers.
Dividing Monomials
For all integers “m” and “n” and any nonzero number “a” ……
Let's review the rules.
m
n
a
a
m na When the problems look like this, and the bases are the same, you will subtract the exponents.
0 1a ANY number raised to the zero power is equal to ONE.
na 1na
If the exponent is negative, it is written on the wrong side of the fraction bar, move it to the other side, and change the sign.
1. 3 2 2f g h
fgh
3 1 2 1 2 1f g h 2 1 1f g h
2. 3 5
7
24
6
x y
xy
Subtract the exponents
42x
2y
Reminder: Never finish a problem with negative
exponents
3. 0 4 2
2 3 2
5 t wu
t w u
1
4. 4 5
2 6
27
9
x y
x y
Subtract the exponents
3 2xy
U’s cancelEach other
2t2w