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Algebra 1
Extra #1.2 Review
Multiplying and
Dividing Polynomials
Multiplication Properties of Exponents
x2 · x3 = x5 (when multiplying with the same base, add the exponents)
(x2)3 = x6
(when there is a power to a power, multiply the exponents)
(xy)3 = x3y3
(take everything inside the parentheses to the exponent on the outside)
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Simplify each expression.
x 2 · x3 = x 5
(x2)3 = x6
(xy)3 = x3y3
1. a5(a)(a7)
2. (x3y4)(xy3)
= a13 add exponents when multiplying
= x4y7 add exponents when multiplying
3. (-3mp2)(5m3p2)
= -15m4p4 add exponents
4. (3n3t2)(-4n3t2)
= (9t2n)(-4n3t2) multiplied 3 by 3
= -36t4n4 add exponents
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5. (3x2y4)3
= 27x6y12
take everything in
parentheses to the 4th
multiply exponents when
you take a power to a power





2

2
1
3
6. w   6w 4 



2  







1
6  
 w  36w 8 

4  
= 9w14
take everything in parentheses
to the exponent on the outside
add exponents when multiplying
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Division Properties of Exponents
x5
x2 = x3
x 2
x2
= 2
y
y
(when dividing, subtract the exponents)
(take everything inside the parentheses to the
exponent on the outside)
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Simplify.
10
6
7.
67
= 63 subtract exponents when dividing
= 216
5
12ab
8.
4a 4 b3
2
3b
 3
a
reduce and cancel
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2 4

9x
y
9.
18x 5 y 4z3

1
2x 3z3
reduce and cancel
10. a5 b0 a-7
= a-2 b0 = 1, add exponents when multiplying
make the negative exponent positive,
 12 to
a move it into the denominator
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11.






3  3
a 
2 
b 
9
a
 6
b
take everything in parentheses
to the -3 power {multiply exponents
for a power to a power}
6
b
 9
a
to make a negative exponent positive
either move it up or down, depending
on where it is






1
2 0
12. 5n m
2nm  2
= 1




anything to the
zero power is 1
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Algebra 1
Extra #1.2
Assignment
Simplify each expression.
1.) (r3t4)(r4t4)
4.)
x3(x4y3)
3 3
7.) (x) y
x 3 y6
10.)


 2x 


 y 3 


2.) (bc3)(b4c3)
3.) [(33)2]2
5.)  3 a a 2b3c4 

4 
6 5
b
c
6.)
b3c 2
5
8.) 24x
 8x 2
9.)

2 4
 2a b

 3a 3b






2
2
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