Transcript Multiplication Powers of Exponents

8.1
Multiplication
Properties of
Exponents
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.
Exponent Vocabulary
an = a • a • a…..a n times
Base number: the number being
multiplied. a is the base
number.
Power: the number of times the
base is multiplied. n is the
power.
Rules for multiplying with exponents
when you have the SAME BASE!
PRODUCT OF
POWERS PROPERTY
Multiplication with the same base:
am • an = am+n add exponents
POWER OF POWER
PROPERTY
Powers of powers with the
same base:
m
n
mn
(a ) = a
multiply exponents
Power of a Product
Property
Different bases, distribute power to each
base and multiply.
Examples:
(a • b)4 = a4 • b4
(-3x)2 = (-3) 2• x 2
= 9x2
= a 4 b4
Try these!
1.
69 =
5
4
66
10,077,696
3. (2x)3
23x3
=
2.
2
9
10 10
1011 = 100,000,000,000
4. [(5x)3]6
8x3
(5x)18 = 5 18 x18
Something fun to do with exponents…
a>1 the equation is a model for
exponential growth.
a<1 the equation is a model for
exponential decay.
Example: ax
2x
Growth
0.6x Decay
Graph
Some final exponent
practice problems…
3y2(2y)3
3y2 23y3
=3
23y5
=24y5
(r2st3)2(s4t)3
= r4s2t6s12t3
= r4s14t9