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Exponents
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Exponents
We write the quantity A multiplied to itself N times as AN, =
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Exponents
We write = the quantity A multiplied to itself N times as AN, i.e.
        = ;            &n= bsp;            = ; 
        = ;            &n= bsp;        A x A x A ….x A =3D AN
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base
exponent
Exponents
We write = the quantity A multiplied to itself N times as AN, i.e.
        = ;            &n= bsp;            = ; 
        = ;            &n= bsp;        A x A x A ….x A =3D AN
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Example A.
4= 3
base
exponent
Exponents
We write = the quantity A multiplied to itself N times as AN, i.e.
        = ;            &n= bsp;            = ; 
        = ;            &n= bsp;        A x A x A ….x A =3D AN
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Example A.
4= 3 =3D (4)(= 4)(4) =3D 64
base
exponent
Exponents
We write = the quantity A multiplied to itself N times as AN, i.e.
        = ;            &n= bsp;            = ; 
        = ;            &n= bsp;        A x A x A ….x A =3D AN
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Example A.
4= 3 =3D (4)(= 4)(4) =3D 64        = ;      
(xy)2
base
exponent
Exponents
We write = the quantity A multiplied to itself N times as AN, i.e.
        = ;            &n= bsp;            = ; 
        = ;            &n= bsp;        A x A x A ….x A =3D AN
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Example A.
4= 3 =3D (4)(= 4)(4) =3D 64        = ;      
(xy)2=3D (xy)= (xy)
base
exponent
Exponents
We write = the quantity A multiplied to itself N times as AN, i.e.
        = ;            &n= bsp;            = ; 
        = ;            &n= bsp;        A x A x A ….x A =3D AN
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Example A.
4= 3 =3D (4)(= 4)(4) =3D 64        = ;      
(xy)2=3D (xy)= (xy) =3D x2y= 2
base
exponent
Exponents
We write = the quantity A multiplied to itself N times as AN, i.e.
        = ;            &n= bsp;            = ; 
        = ;            &n= bsp;        A x A x A ….x A =3D AN
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Example A.
4= 3 =3D (4)(= 4)(4) =3D 64        = ;      
(xy)2=3D (xy)= (xy) =3D x2y= 2
xy2
base
exponent
Exponents
We write = the quantity A multiplied to itself N times as AN, i.e.
        = ;            &n= bsp;            = ; 
        = ;            &n= bsp;        A x A x A ….x A =3D AN
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Example A.
4= 3 =3D (4)(= 4)(4) =3D 64        = ;      
(xy)2=3D (xy)= (xy) =3D x2y= 2
xy2 =3D (x)(= yy)
base
exponent
Exponents
We write = the quantity A multiplied to itself N times as AN, i.e.
        = ;            &n= bsp;            = ; 
        = ;            &n= bsp;        A x A x A ….x A =3D AN
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Example A.
4= 3 =3D (4)(= 4)(4) =3D 64        = ;      
(xy)2=3D (xy)= (xy) =3D x2y= 2
xy2 =3D (x)(= yy)
–x= 2 =3D R= 11;(xx)
base
exponent
Exponents
We write = the quantity A multiplied to itself N times as AN, i.e.
        = ;            &n= bsp;            = ; 
        = ;            &n= bsp;        A x A x A ….x A =3D AN
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Example A.
4= 3 =3D (4)(= 4)(4) =3D 64        = ;      
(xy)2=3D (xy)= (xy) =3D x2y= 2
xy2 =3D (x)(= yy)
–x= 2 =3D R= 11;(xx)
base
exponent
Exponents
We write = the quantity A multiplied to itself N times as AN, i.e.
        = ;            &n= bsp;            = ; 
        = ;            &n= bsp;        A x A x A ….x A =3D AN
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Example A.
4= 3 =3D (4)(= 4)(4) =3D 64        = ;      
(xy)2=3D (xy)= (xy) =3D x2y= 2
xy2 =3D (x)(= yy)
–x= 2 =3D R= 11;(xx)
base
exponent
Exponents
Rules of Exponents
We write = the quantity A multiplied to itself N times as AN, i.e.
        = ;            &n= bsp;            = ; 
        = ;            &n= bsp;        A x A x A ….x A =3D AN
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Example A.
4= 3 =3D (4)(= 4)(4) =3D 64        = ;      
(xy)2=3D (xy)= (xy) =3D x2y= 2
xy2 =3D (x)(= yy)
–x= 2 =3D R= 11;(xx)
base
exponent
Exponents
Multiplication Rule: ANAK =3DAN+K 
Rules of Exponents
We write = the quantity A multiplied to itself N times as AN, i.e.
        = ;            &n= bsp;            = ; 
        = ;            &n= bsp;        A x A x A ….x A =3D AN
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Example A.
4= 3 =3D (4)(= 4)(4) =3D 64        = ;      
(xy)2=3D (xy)= (xy) =3D x2y= 2
xy2 =3D (x)(= yy)
–x= 2 =3D R= 11;(xx)
base
exponent
Exponents
Multiplication Rule: ANAK =3DAN+K 
Example B.
 
a. 5354
Rules of Exponents
We write = the quantity A multiplied to itself N times as AN, i.e.
        = ;            &n= bsp;            = ; 
        = ;            &n= bsp;        A x A x A ….x A =3D AN
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Example A.
4= 3 =3D (4)(= 4)(4) =3D 64        = ;      
(xy)2=3D (xy)= (xy) =3D x2y= 2
xy2 =3D (x)(= yy)
–x= 2 =3D R= 11;(xx)
base
exponent
Exponents
Multiplication Rule: ANAK =3DAN+K 
Example B.
 
a. 5354 =3D (5*5*5)(5= *5*5*5) <= span lang=3DEN-US style=3D'mso-hansi-font-family:Arial;font-size:133%;color:#02= 3006; mso-fareast-language:ZH-CN;mso-special-format:lastCR;display:none'>
Rules of Exponents
We write = the quantity A multiplied to itself N times as AN, i.e.
        = ;            &n= bsp;            = ; 
        = ;            &n= bsp;        A x A x A ….x A =3D AN
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Example A.
4= 3 =3D (4)(= 4)(4) =3D 64        = ;      
(xy)2=3D (xy)= (xy) =3D x2y= 2
xy2 =3D (x)(= yy)
–x= 2 =3D R= 11;(xx)
base
exponent
Exponents
Multiplication Rule: ANAK =3DAN+K 
Example B.
 
a. 5354 =3D (5*5*5)(5= *5*5*5) =3D 53+4 =3D 57
b. x= 5y7x4y6
Rules of Exponents
We write = the quantity A multiplied to itself N times as AN, i.e.
        = ;            &n= bsp;            = ; 
        = ;            &n= bsp;        A x A x A ….x A =3D AN
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Example A.
4= 3 =3D (4)(= 4)(4) =3D 64        = ;      
(xy)2=3D (xy)= (xy) =3D x2y= 2
xy2 =3D (x)(= yy)
–x= 2 =3D R= 11;(xx)
base
exponent
Exponents
Multiplication Rule: ANAK =3DAN+K 
Example B.
 
a. 5354 =3D (5*5*5)(5= *5*5*5) =3D 53+4 =3D 57
b. <= span lang=3DEN-US style=3D'mso-fareast-font-family:\5B8B\4F53;mso-hansi-font-fa= mily: Arial;font-size:133%;color:red;mso-fareast-language:ZH-CN'>x5y7x4y6 =3D = x5x4y7y6
Rules of Exponents
We write = the quantity A multiplied to itself N times as AN, i.e.
        = ;            &n= bsp;            = ; 
        = ;            &n= bsp;        A x A x A ….x A =3D AN
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Example A.
4= 3 =3D (4)(= 4)(4) =3D 64        = ;      
(xy)2=3D (xy)= (xy) =3D x2y= 2
xy2 =3D (x)(= yy)
–x= 2 =3D R= 11;(xx)
base
exponent
Exponents
Multiplication Rule: ANAK =3DAN+K 
Example B.
 
a. 5354 =3D (5*5*5)(5= *5*5*5) =3D 53+4 =3D 57
b. <= span lang=3DEN-US style=3D'mso-fareast-font-family:\5B8B\4F53;mso-hansi-font-fa= mily: Arial;font-size:133%;color:red;mso-fareast-language:ZH-CN'>x5y7x4y6 =3D = x5x4y7y6 =3D x9y13 
Rules of Exponents
We write = the quantity A multiplied to itself N times as AN, i.e.
        = ;            &n= bsp;            = ; 
        = ;            &n= bsp;        A x A x A ….x A =3D AN
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Example A.
4= 3 =3D (4)(= 4)(4) =3D 64        = ;      
(xy)2=3D (xy)= (xy) =3D x2y= 2
xy2 =3D (x)(= yy)
–x= 2 =3D R= 11;(xx)
base
exponent
Exponents
Multiplication Rule: ANAK =3DAN+K 
Example B.
 
a. 5354 =3D (5*5*5)(5= *5*5*5) =3D 53+4 =3D 57
b. <= span lang=3DEN-US style=3D'mso-fareast-font-family:\5B8B\4F53;mso-hansi-font-fa= mily: Arial;font-size:133%;color:red;mso-fareast-language:ZH-CN'>x5y7x4y6 =3D = x5x4y7y6 =3D x9y13 
Rules of Exponents
Divisi= on Rule:<= /div>
AA
=3D A 
We write = the quantity A multiplied to itself N times as AN, i.e.
        = ;            &n= bsp;            = ; 
        = ;            &n= bsp;        A x A x A ….x A =3D AN
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Example A.
4= 3 =3D (4)(= 4)(4) =3D 64        = ;      
(xy)2=3D (xy)= (xy) =3D x2y= 2
xy2 =3D (x)(= yy)
–x= 2 =3D R= 11;(xx)
base
exponent
Exponents
Multiplication Rule: ANAK =3DAN+K 
Example B.
 
a. 5354 =3D (5*5*5)(5= *5*5*5) =3D 53+4 =3D 57
b. <= span lang=3DEN-US style=3D'mso-fareast-font-family:\5B8B\4F53;mso-hansi-font-fa= mily: Arial;font-size:133%;color:red;mso-fareast-language:ZH-CN'>x5y7x4y6 =3D = x5x4y7y6 =3D x9y13 
Rules of Exponents
Divisi= on Rule:<= /div>
Example C. =
AA
=3D A 
56
52
We write = the quantity A multiplied to itself N times as AN, i.e.
        = ;            &n= bsp;            = ; 
        = ;            &n= bsp;        A x A x A ….x A =3D AN
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Example A.
4= 3 =3D (4)(= 4)(4) =3D 64        = ;      
(xy)2=3D (xy)= (xy) =3D x2y= 2
xy2 =3D (x)(= yy)
–x= 2 =3D R= 11;(xx)
base
exponent
Exponents
Multiplication Rule: ANAK =3DAN+K 
Example B.
 
a. 5354 =3D (5*5*5)(5= *5*5*5) =3D 53+4 =3D 57
b. <= span lang=3DEN-US style=3D'mso-fareast-font-family:\5B8B\4F53;mso-hansi-font-fa= mily: Arial;font-size:133%;color:red;mso-fareast-language:ZH-CN'>x5y7x4y6 =3D = x5x4y7y6 =3D x9y13 
Rules of Exponents
Divisi= on Rule:<= /div>
Example C. =
AA
=3D A 
56
52
=3D= 3;
(5)(5)(5)(5)(5)(5)
(5)(5)
We write = the quantity A multiplied to itself N times as AN, i.e.
        = ;            &n= bsp;            = ; 
        = ;            &n= bsp;        A x A x A ….x A =3D AN
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Example A.
4= 3 =3D (4)(= 4)(4) =3D 64        = ;      
(xy)2=3D (xy)= (xy) =3D x2y= 2
xy2 =3D (x)(= yy)
–x= 2 =3D R= 11;(xx)
base
exponent
Exponents
Multiplication Rule: ANAK =3DAN+K 
Example B.
 
a. 5354 =3D (5*5*5)(5= *5*5*5) =3D 53+4 =3D 57
b. <= span lang=3DEN-US style=3D'mso-fareast-font-family:\5B8B\4F53;mso-hansi-font-fa= mily: Arial;font-size:133%;color:red;mso-fareast-language:ZH-CN'>x5y7x4y6 =3D = x5x4y7y6 =3D x9y13 
Rules of Exponents
Divisi= on Rule:<= /div>
Example C. =
AA
=3D A 
56
52
=3D= 3;
(5)(5)(5)(5)(5)(5)
(5)(5)
We write = the quantity A multiplied to itself N times as AN, i.e.
        = ;            &n= bsp;            = ; 
        = ;            &n= bsp;        A x A x A ….x A =3D AN
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Example A.
4= 3 =3D (4)(= 4)(4) =3D 64        = ;      
(xy)2=3D (xy)= (xy) =3D x2y= 2
xy2 =3D (x)(= yy)
–x= 2 =3D R= 11;(xx)
base
exponent
Exponents
Multiplication Rule: ANAK =3DAN+K 
Example B.
 
a. 5354 =3D (5*5*5)(5= *5*5*5) =3D 53+4 =3D 57
b. <= span lang=3DEN-US style=3D'mso-fareast-font-family:\5B8B\4F53;mso-hansi-font-fa= mily: Arial;font-size:133%;color:red;mso-fareast-language:ZH-CN'>x5y7x4y6 =3D = x5x4y7y6 =3D x9y13 
Rules of Exponents
Divisi= on Rule:<= /div>
Example C. =
AA
=3D A 
56
52
=3D= 3;
(5)(5)(5)(5)(5)(5)
(5)(5)
=3D 56 – 2 =3D 54
We write = the quantity A multiplied to itself N times as AN, i.e.
        = ;            &n= bsp;            = ; 
        = ;            &n= bsp;        A x A x A ….x A =3D AN
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Power = Rule: (AN)K =3D ANK&#= 13;
Exponents
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Power = Rule: (AN)K =3D ANK&#= 13;
Example D.  (34)5
Exponents
A
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Power = Rule: (AN)K =3D ANK&#= 13;
Example D.  (34)5 =3D (34)(34)(34)(34)(34)
Exponents
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Power = Rule: (AN)K =3D ANK&#= 13;
Example D.  (34)5 =3D (34)(34)(34)(34)(34)  =3D 34+4+4+4+4
Exponents
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Power = Rule: (AN)K =3D ANK&#= 13;
Example D.  (34)5 =3D (34)(34)(34)(34)(34)  =3D 34+4+4+4+4 =3D 34*5 =3D 320
Exponents
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Power = Rule: (AN)K =3D ANK&#= 13;
Example D.  (34)5 =3D (34)(34)(34)(34)(34)  =3D 34+4+4+4+4 =3D 34*5 =3D 320
Exponents
Since       =3D= 1
A
A
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Power = Rule: (AN)K =3D ANK&#= 13;
Example D.  (34)5 =3D (34)(34)(34)(34)(34)  =3D 34+4+4+4+4 =3D 34*5 =3D 320
Exponents
Since       =3D= 1 =3D A1 – 1 
A
A
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Power = Rule: (AN)K =3D ANK&#= 13;
Example D.  (34)5 =3D (34)(34)(34)(34)(34)  =3D 34+4+4+4+4 =3D 34*5 =3D 320
Exponents
Since       =3D= 1 =3D A1 – 1 =3D A0
A
A
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Power = Rule: (AN)K =3D ANK&#= 13;
Example D.  (34)5 =3D (34)(34)(34)(34)(34)  =3D 34+4+4+4+4 =3D 34*5 =3D 320
Exponents
Since       =3D= 1 =3D A1 – 1 =3D A0, we obtain the 0-power Rule.
A
A
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Power = Rule: (AN)K =3D ANK&#= 13;
Example D.  (34)5 =3D (34)(34)(34)(34)(34)  =3D 34+4+4+4+4 =3D 34*5 =3D 320
Exponents
Since       =3D= 1 =3D A1 – 1 =3D A0, we obtain the 0-power Rule.
A
A
0-Powe= r Rule:  A0 =3D 1
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Power = Rule: (AN)K =3D ANK&#= 13;
Example D.  (34)5 =3D (34)(34)(34)(34)(34)  =3D 34+4+4+4+4 =3D 34*5 =3D 320
Exponents
Since       =3D= 1 =3D A1 – 1 =3D A0, we obtain the 0-power Rule.
A
A
0-Powe= r Rule:  A0 =3D 1
Since       =3D=      
1
A
A
A
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Power = Rule: (AN)K =3D ANK&#= 13;
Example D.  (34)5 =3D (34)(34)(34)(34)(34)  =3D 34+4+4+4+4 =3D 34*5 =3D 320