Transcript LAWS OF EXPONENTS - Thomasville High School

Exponents
•
For all real numbers x and all positive
integers m,
xm = x • x • x •…• x,
m factors
Evaluate:
1. 28
2. 53
3. 34
Answers:
1. 256 2. 125
3. 81
4. 6
4. 61
PRODUCT OF POWERS
• Product of Powers Property
For all real numbers x and all integers m
and n,
m
x
•
n
x
=
m+n
x
KEEP the BASE then
ADD the EXPONENTS!
Example:
Simplify the following:
5
2 •
4
2
1.
3
2. 8 • 8
3. y2 • y5
4. 5m • 5p
6
3
5. z • z
z
3
6. a • a
25 + 4 = 29 = 512
81 + 3 = 84 = 4096
y2 + 5 = y7
5m + p
z 6 + 3 = z9
az + 3
Multiplying Monomials
•
Definition
Monomial
- A monomial is an algebraic expression
that is either a constant, a variable, or a
product of a constant and one or more
variables. The constant is called
coefficient.
To simplify a product of monomials,
1. Multiply the coefficients.
2. Add the exponents of the same variables.
Examples:
Simplify.
1. (5x)(-30x2)
2.
(-4a2b)(-ac2)(3b2c2)
3. (3m2)(60mp2)
-150x3
12a3b3c4
180m3p2
Simplify.
3.
(8xz)(-10y)(-2yz2)
4. (3xy2)(-5x2y)(y3z)
5.
(-2c2)(3x3)
6.
(3xaybzc)(-ynzm)
160xy2z3
-15x3y6z
-6c2x3
-3xa yb + nzc + m
Geometry Connection
The volume, V, of a right rectangular prism
can be found by using the formula V = lwh,
where l is the length, w is the width and h
is the height. Suppose that the prism has a
length of 2xy, a width of 3xy, and a height
of 6xyz. Find the volume.
Solution:
V = lwh
= (2xy)(3xy)(6xyz)
V = 36x3y3z
Geometry Connection
The area, A, of a trapezoid can be found by
using the formula A = ½ h(b1 + b2), where
b1 is one base and b2 is the other base, and
h is the height. Suppose that a trapezoid
has a base of 5x, another base of 9x, and a
height of 8xy. Find the area.
Solution:
A = ½ h(b1 + b2),
= ½ (8xy)(5x + 9x)
= ½ (8xy)(14x)
A = 56x2y
Do these…
1. The volume, V, of a right rectangular
prism can be found by using the formula
V = lwh, where l is the length, w is the
width and h is the height. Suppose that
the prism has a length of 3rt, a width of
5rt, and a height of 2rty. Find the
volume.
Answer: 30r3t3y
2. The area, A, of a triangle can be found
using the formula A = ½ bh, where b is
the base and h is the height of the
triangle. Find the area of a triangle with
base 10x2y and height 7x3y5.
Answer: 35x5y6
Time to do your work….
• Get a sheet of paper and do the assigned
CLASSWORK!
• WORK SILENTLY!!!!