Transcript Multiplying Monomials

Do Now
Is the data qualitative or quantitative?
1) The heights of everyone in the class.
2) The favorite television shows of everyone in the
class.
Would the data need to be univariate or bivariate?
3) Does the number of hours a student studies
improve his/her final examination scores?
4) Find the mean of the scores on the last math test.
Is the situation biased?
5)
A study is conducted to determine the number of
students who wore a free promotional T-shirt given to all
students at a local university rock concert. Five hundred
students were chosen at random from the 5000 students
attending the concert and asked if they wore the T-shirt
during the concert.
6)
A study is conducted to estimate the average speed of
drivers using the fast lane of the highway. To determine
the drivers' speeds, a police car will follow the drivers on
the highway and record their speeds using the police
car's speedometer.
A monomial is a single term, it can be
1. a number,
2. a variable, or
3. a product of one or more
numbers and variables.
Examples:
5
y
3x2y3
Why are the following not
monomials?
x+y
addition
x
y
division
2 - 3a
subtraction
Multiplying Monomials
When multiplying monomials, you
1) MULTIPLY the coefficients
2) ADD the exponents.
1) x2 • x4
x2+4
x6
2) 2a2y3 • 3a3y4
6a5y7
Simplify
1.
2.
3.
4.
m7
m8
12
m
13
m
3
4
m (m )(m)
Raising Monomials To A Power
When you raise a monomial to a power,
you first rewrite the problem, then
multiply.
1) (x3)2
(x3) (x3)
x6
2) (y2)4
(y2) (y2) (y2) (y2)
y8
Simplify
1.
2.
3.
4.
p2
p4
8
p
16
p
4
4
(p )
More Practice
1) (2a)3
(2a) (2a) (2a)
8a3
2) (3x)2
(3x) (3x)
9x2
Simplify
1.
2.
3.
4.
12r3
12r4
3
64r
4
64r
3
(4r)
Even More Practice
1) (x3y2)2
(x3y2) (x3y2)
x6 y4
2) (-4x4y3)3
(-4x4y3) (-4x4y3) (-4x4y3)
- 64x12y9
Simplify
1.
2.
3.
4.
12a8b12
81a6b7
16
81
81a b
8
12
81a b
2
3
4
(3a b )
* Always start with the exponents
outside the ( ) !!!!
1) (3x2y3)2(4xy)
(3x2y3) (3x2y3) (4xy)
36x5 y7
2) (4xy)2 (-2x2)3
(4xy) (4xy) (-2x2) (-2x2) (-2x2)
- 128x8y2