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Transcript of Name: Date: Period: Topic: Multiplication & Division Properties of Exponents Essential Question: How...
Name: Date:Period:Topic: Multiplication & Division Properties of ExponentsEssential Question: How can you use the multiplication and/or division properties of exponents to simplify problems?
Warm-Up:Mix-Review
Explain how do you determine if a problem
is a function, provide an example.
I should use my notesto refresh my memory!
Home-Learning review #7
Quick Review:(Lets Keep it Under a Minute)!
Location of Exponent
• An exponent is a little number high and to the right of a regular or base number.
3 4Base
Exponent
Definition of Exponent
• An exponent tells how many times a number is multiplied by itself.
3 4Base
Exponent
What an Exponent Represents
• An exponent tells how many times a number is multiplied by itself.
34= 3 x 3 x 3 x 3
How to read an Exponent
• This exponent is read three to the fourth power.
3 4Base
Exponent
P ro d u c t o f p o w ers p ro p erty : a a am n m n
P o w er o f a p o w er p ro p erty : a am n m n
P o w er o f a p ro d u c t p ro p erty : a b a bm m m
Words Numbers Algebra
To multiply powers with the
same base, keep the base and add the exponents.
bm • bn = bm + n
35 • 38 = 35 + 8 = 313
MULTIPLYING POWERS WITH THE SAME BASE
1. 66 • 63
2. n5 • n7
3. 25 • 2
4. 244 • 244
5. 42 • 44
6. x2 • x3
7. x5 • y2
8. 412 • 417
Together! Alone!
15
5•3
53
4
4
)4(
NOTE:
Multiply the exponents, not add them!
Words Numbers Algebra
To multiply power of a
power, keep the base and
multiply the exponents.
Multiplying Power of a Power
(pr)s =
pr • s
Together! Alone!
1. (x2)3
2. (55)2
3. (y4)2
4. (3)6
1.) b2 • b7
2.) (p3)4
3.) (a2)3 • a3
4.) x2 • (xy)2
5.) (4m)2 • m3
6.) (3a)3
•(2p)2
7.) w3 • (3w)4
8.) p-2
9.)(a2b)0
10.)(x-2y3)-2 Pair- Practice!
1.) b2 • b7 1.) b9 2.) (p3)4 2.) p12 3.) (a2)3 • a3 3.) a9
4.) x2 • (xy)2 4.) x4y2 5.) (4m)2 • m3 5.) 16m5
6.) (3a)3 • (2p)2 6.) 108a3p2 7.) w3 • (3w)4 7.) 81w7 8.) p-2 8.) 1/p2 9.)(a2b)0 9.) 1 10.)(x-2y3)-2 10.) x4/y6
ANSWERS
Multiplying Polynomials:
In multiplying polynomials, you have to multiply the
coefficients and add up the exponents of the variables
with the same base.
Ex:
35
3
2
5
32
232
20
•
•
20
5•4
45
yx
y
yy
x
xx
yxyx
Please simplify the following equations:
)3)(4( 3224 yxyx
Answer: 5612 yx
How?:
56
5
32
6
24
12
•
•
12
3•4
yx
y
yy
x
xx
Additional Practice:
Page 429 - 431 (8, 9, 16, 47, 49, 73)
Page 436 - 437 (20, 47)
Division Properties of Exponents
Simplify
Finding Quotients of Powers
A.
B.
Together Alone
C.
D.
A.
B.
C.
D.
Simplify.
Finding Positive Powers of Quotient
A.
B.
Together Alone
C.
A.
B.
C.
Remember that What if x is a fraction?
Simplify.
Finding Negative Powers of Quotients
A.
B.
Together Alone
C.
A.
B.
C.
Additional Practice:
Page 443 - 445 (8, 11, 13, 37, 42, 49, 50, 60)
Home-Learning Assignment #8:
Page 429 - 431 (25, 48, 50, 72)Page 437 – 438 (48, 78)
Page 443 - 445 (14, 16, 43, 70)