Transcript Division Properties of Exponents

8.3 Division
Properties of
Exponents
Learn to use the division
properties of exponents to
evaluate powers and
simplify expressions.
Focus 8 Learning Goal – (HS.N-RN.A.1 & 2, HS.A-SSE.B.3, HS.A-CED.A.2, HS.F-IF.B.4, HS.FIF.C.8 & 9, and HS.F-LE.A.1) = Students will construct, compare and interpret
linear and exponential function models and solve problems in context
with each model.
4
3
2
1
0
In addition to level
3, students make
connections to
other content areas
and/or contextual
situations outside
of math.
Students will construct,
compare, and interpret linear
and exponential function
models and solve problems in
context with each model.
- Compare properties of 2
functions in different ways
(algebraically, graphically,
numerically in tables, verbal
descriptions)
- Describe whether a
contextual situation has a linear
pattern of change or an
exponential pattern of change.
Write an equation to model it.
- Prove that linear functions
change at the same rate over
time.
- Prove that exponential
functions change by equal
factors over time.
- Describe growth or decay
situations.
- Use properties of exponents
to simplify expressions.
Students will
construct,
compare, and
interpret linear
function models
and solve
problems in
context with the
model.
- Describe a
situation where
one quantity
changes at a
constant rate per
unit interval as
compared to
another.
Students will have
partial success at
a 2 or 3, with
help.
Even with help,
the student is not
successful at the
learning goal.
Reduce
25
23
= 22222
222
=22 = 4
Rules for Division
Let a and b any real number,
and m and n be integers.
Quotient of Powers Property:
Subtract n from m (a0)
am
m-n
=
a
an
Rules for Division
Power of Quotient Property:
Distribute power across the ( ).
a
b
m
m
a
= m
b
*Remember: a negative exponent
means to rewrite its reciprocal!!
Practice
1.
37
34
= 33
828
2.
85
3.
2
3
= 27
= 83 = 8-2 = 1
82
85
2
= 22
32
=4
9
=1
64
Try the Challenge Problem
16x3y ∙ -2xy Multiply straight across to
make one fraction.
3
-4xy
-x
-32x4y2
Divide whole numbers
2
3
4x y
exponents and
-8x4y2 Subtract
2
make sure all exponents in
-8x
x2y3 your answer are positive.
y
Review all of the
rules for exponents:
http://safeshare.tv/w/LzzdFknWAc
Super Base!