Chapter 8 Review Laws of Exponents. LAW #1 Product law: add the exponents together when multiplying...
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Transcript of Chapter 8 Review Laws of Exponents. LAW #1 Product law: add the exponents together when multiplying...
LAW #1 Product law:
add the exponents together when multiplying the powers with the same base.
Ex:NOTE:
This operation can only be done if the base is the same!
SIMPLIFY THESE ON YOUR OWN:
€
x 3 • x 5
€
x 3y 4( ) x
2y 5( )
€
x 8
€
x 5y 9
€
33 • 312
= 33+12
= 315
LAW #2 Power of a power:
keep the base and multiply the exponents.
Ex: NOTE:
Multiply the exponents, not add them!SIMPLIFY THESE ON YOUR OWN:
€
x 3( )
5
€
x 3y 4( )
4
€
x15
€
x12y16
€
43( )
5
= 43• 5
= 415
LAW #3 Power of a product:
Distribute the power to each number or variable in the parentheses.
Ex: NOTE:
Multiply the exponents, not add them!
SIMPLIFY THESE ON YOUR OWN:
€
−2a( )2
€
3x 3y 4( )
2
€
=(−2)2a2
= 4a2
€
9x 6y 8
€
4x( )3
= 43 x 3
= 64x 3
LAW #4 Zero exponent law:
Any power raised to an exponent of zero equals one.
Ex:
SIMPLIFY THESE ON YOUR OWN:
€
x 3( )
0
€
24xy 8( )
0
€
1
€
1
€
1,283,249x 3( )
0
=1
LAW #5 Negative exponents:
To make an exponent positive, flip the base.
Ex:NOTE:
This does not change the sign of the base.
SIMPLIFY THESE ON YOUR OWN:
€
x −3
€
2x 3y 4( )
−2
€
1
x 3
€
=2−2 x −6y −8
=1
22 x 6y 8
=1
4x 6y 8
€
2−4
=1
24
=1
16
LAW #6 Quotient Property
Subtract “TOP EXPONENT MINUS THE BOTTOM EXPONENT”
Ex:NOTE:
This operation can only be done if the base is the same!
SIMPLIFY THESE ON YOUR OWN:
€
4a5
a2
€
3y 3
y 7
€
4a3
€
3y −4
€
3
y 4€
312
34
= 312−4
= 38
LAW #7 Quotient Property
Distribute the power to the top and bottom of the quotient.
Ex:
SIMPLIFY THESE ON YOUR OWN:
€
2x
3
⎛
⎝ ⎜
⎞
⎠ ⎟3
€
−2a
b
⎛
⎝ ⎜
⎞
⎠ ⎟−4
€
23 x 3
33
⎛
⎝ ⎜
⎞
⎠ ⎟
€
(−2)−4 a−4
b−4
€
8x 3
27
⎛
⎝ ⎜
⎞
⎠ ⎟
€
b4
(−2)4 a4
€
b4
16a4
€
x
2
⎛
⎝ ⎜
⎞
⎠ ⎟3
=x 3
23
=x 3
8
More examples on your own:
Ex 1:
Ex 2:
Ex 3:
Ex 4:
Ex 5:
Ex 6:
Ex 7:
Ex 8:
€
b7 • b2
€
p3( )
4
€
a2( )
3• a3
€
x 2 • xy( )2
€
4m( )2
• m3
€
3a( )3
• 2p( )2
€
82 • xy( )2
• 2x
€
q0
€
b9
€
p12
€
a9
€
x 4y 2
€
16m5
€
108a3p2
€
128x 3y 2
€
1
More examples on your own:
Ex 9:
Ex 10:
Ex 11:
Ex 12:
Ex 13:
Ex 14:
Ex 15:
Ex 16:
€
5x 2y( ) 4x 3y 2( )
€
25x 5y 4
5x 4y 2
€
x 2 • x 3
€
x13
x 5
€
55( )
2
€
5−3
€
4x 4y 2( ) 3x 2y 3
( )
€
12x 3y 4
4x 2y 2
€
20x 5y 3
€
5xy 2
€
x 5
€
x 8
€
510
= 9,765,625
€
1
53 =1
125
€
12x 6y 5
€
3xy 2
More examples on your own:
Ex 17:
Ex 18:
Ex 19:
Ex 20:
Ex 21:
Ex 22:
Ex 23:
Ex 24:
€
w3 • 3w( )4
€
p−2
€
a2b( )0
€
x −2y 3( )
−2
€
p4
p2
€
3b2
9b5
€
4x 2( )
2
4x 4
€
32 x 2y 0
x 3y −4
€
81w7
€
1
p2
€
1
€
x 4
y 6
€
p2
€
1
3b3
€
4
€
9y 4
x
More examples on your own:
Ex 25:
Ex 26:
Ex 27:
Ex 28:
Ex 29:
Ex 30:
Ex 31:
Ex 32:
€
m
n
⎛
⎝ ⎜
⎞
⎠ ⎟3
• m2n−4
€
3a2
b
⎛
⎝ ⎜
⎞
⎠ ⎟
3
•2b−1
9a
€
3
4
⎛
⎝ ⎜
⎞
⎠ ⎟3
€
2 + 3(4)2
€
m5
n7
€
6a5
b4
€
27
64
€
50
Express each number in scientific notation:
1.) 6,300 2.) 4,600,000
3.) 0.00013 4.) 0.000009
6.3 x 1034.6 x 106
1.3 x 10-4 9 x 10-6
Express each number in decimal form:
1.) 4.5 x 106 2.) 3 x 10-4
3.) 2.36 x 100 4.) 9.1 x 10-1
4,500,000 0.0003
2.36 0.91