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Exponents and Radicals
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= We write A= x A x A ….x A =3D An where n is= the number of = A's.
Exponents and Radicals
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Multiplication Rule:  AnA =3DAn+k =
Division Rule:      =   =3D An – k      
An
Ak
Power Rule:  (An)k =3D Ank
= We write A= x A x A ….x A =3D An where n is= the number of = A's.
Exponents and Radicals
Rules of Exponents:
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Multiplication Rule:  AnA =3DAn+k =
Division Rule:      =   =3D An – k      
Example A: <= /span>
a. 535 =3D   <= /span>
An
Ak
b.       =3D=
57
54
Power Rule:  (An)k =3D Ank
c. (34)2 =3D
= We write A= x A x A ….x A =3D An where n is= the number of = A's.
Exponents and Radicals
Rules of Exponents:
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Multiplication Rule:  AnA =3DAn+k =
Division Rule:      =   =3D An – k      
Example A: <= /span>
a. 535 =3D 53+4 =3D 5  
An
Ak
b.       =3D=   
57
54
Power Rule:  (An)k =3D Ank
c. (34)2 =3D
= We write A= x A x A ….x A =3D An where n is= the number of = A's.
Exponents and Radicals
Rules of Exponents:
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Multiplication Rule:  AnA =3DAn+k =
Division Rule:      =   =3D An – k      
Example A: <= /span>
a. 535 =3D 53+4 =3D 5  
An
Ak
b.       =3D= 57–4 =3D 53    
57
54
Power Rule:  (An)k =3D Ank
c. (34)2 =3D
= We write A= x A x A ….x A =3D An where n is= the number of = A's.
Exponents and Radicals
Rules of Exponents:
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Multiplication Rule:  AnA =3DAn+k =
Division Rule:      =   =3D An – k      
Example A: <= /span>
a. 535 =3D 53+4 =3D 5  
An
Ak
b.       =3D= 57–4 =3D 53    
57
54
Power Rule:  (An)k =3D Ank
c. (34)2 =3D 34*2  =3D 38
= We write A= x A x A ….x A =3D An where n is= the number of = A's.
Exponents and Radicals
Rules of Exponents:
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Special Exponent= s
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0-power R= ule :  A0=3D1 &nb= sp; (A=3D0)
Special Exponent= s
------=_NextPart_01C82E61.3C6904C0 Content-Location: file:///C:/E51446F3/1Exponents_files/slide0122_image010.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCAAVAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAgAG ABIAgAAAAAAAAAIUhBFxqJf+TJSNwjrZmglXDV3hthQAOx== ------=_NextPart_01C82E61.3C6904C0 Content-Location: file:///C:/E51446F3/1Exponents_files/slide0123.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Exponents
0-power Rule :  A0=3D1 &nb= sp; (A=3D0)
     Reason: 1 =3D      = 3;
A<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>1&#= 13;
A<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>1&#= 13;
Special Exponent= s
------=_NextPart_01C82E61.3C6904C0 Content-Location: file:///C:/E51446F3/1Exponents_files/slide0123_image011.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCAAVAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAgAG ABIAgAAAAAAAAAIUhBFxqJf+TJSNwjrZmglXDV3hthQAOx== ------=_NextPart_01C82E61.3C6904C0 Content-Location: file:///C:/E51446F3/1Exponents_files/slide0123_image012.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHgADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAAAb AAMAgAAAAAAAAAIIjI+py+0PTwEAOw== ------=_NextPart_01C82E61.3C6904C0 Content-Location: file:///C:/E51446F3/1Exponents_files/slide0124.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Exponents
0-power Rule :  A0=3D1 &nb= sp; (A=3D0)
     Reason: 1 =3D      =3D A1–1 =3D A0  = = 3;
A<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>1&#= 13;
A<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>1&#= 13;
Special Exponent= s
------=_NextPart_01C82E61.3C6904C0 Content-Location: file:///C:/E51446F3/1Exponents_files/slide0124_image013.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCAAVAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAgAG ABIAgAAAAAAAAAIUhBFxqJf+TJSNwjrZmglXDV3hthQAOx== ------=_NextPart_01C82E61.3C6904C0 Content-Location: file:///C:/E51446F3/1Exponents_files/slide0124_image014.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHgADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAAAb AAMAgAAAAAAAAAIIjI+py+0PTwEAOw== ------=_NextPart_01C82E61.3C6904C0 Content-Location: file:///C:/E51446F3/1Exponents_files/slide0125.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Exponents
0-power Rule :  A0=3D1 &nb= sp; (A=3D0)
     Reason: 1 =3D      =3D A1–1 =3D A0  =
Negative Power Rule :<= span style=3D'mso-spacerun:yes'>  A-k =3D
A<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>1&#= 13;
A<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>1&#= 13;
1<= /div>
A<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>k&#= 13;
Special Exponent= s
------=_NextPart_01C82E61.3C6904C0 Content-Location: file:///C:/E51446F3/1Exponents_files/slide0125_image015.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCAAVAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAgAG ABIAgAAAAAAAAAIUhBFxqJf+TJSNwjrZmglXDV3hthQAOx== ------=_NextPart_01C82E61.3C6904C0 Content-Location: file:///C:/E51446F3/1Exponents_files/slide0125_image016.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHgADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAAAb AAMAgAAAAAAAAAIIjI+py+0PTwEAOw== ------=_NextPart_01C82E61.3C6904C0 Content-Location: file:///C:/E51446F3/1Exponents_files/slide0125_image017.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHgAEAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAa AAIAgAAAAAAAAAIGjI+py70FADs= ------=_NextPart_01C82E61.3C6904C0 Content-Location: file:///C:/E51446F3/1Exponents_files/slide0126.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Exponents
0-power Rule :  A0=3D1 &nb= sp; (A=3D0)
     Reason: 1 =3D      =3D A1–1 =3D A0  =
Negative Power Rule :<= span style=3D'mso-spacerun:yes'>  A-k =3D
     Reason:       =3D=        = 3;
A<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>1&#= 13;
A<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>1&#= 13;
1<= /div>
A<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>k&#= 13;
1<= /div>
A<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>k&#= 13;
A<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>0&#= 13;
A<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>k&#= 13;
Special Exponent= s
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0-power Rule :  A0=3D1 &nb= sp; (A=3D0)
     Reason: 1 =3D      =3D A1–1 =3D A0  =
Negative Power Rule :<= span style=3D'mso-spacerun:yes'>  A-k =3D
     Reason:       =3D=        =3D= A0–k =3D A-k
A<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>1&#= 13;
A<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>1&#= 13;
1<= /div>
A<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>k&#= 13;
1<= /div>
A<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>k&#= 13;
A<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>0&#= 13;
A<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>k&#= 13;
Special Exponent= s
------=_NextPart_01C82E61.3C6904C0 Content-Location: file:///C:/E51446F3/1Exponents_files/slide0127_image023.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhCAAVAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAgAG ABIAgAAAAAAAAAIUhBFxqJf+TJSNwjrZmglXDV3hthQAOx== ------=_NextPart_01C82E61.3C6904C0 Content-Location: file:///C:/E51446F3/1Exponents_files/slide0127_image024.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHgADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAAAb AAMAgAAAAAAAAAIIjI+py+0PTwEAOw== ------=_NextPart_01C82E61.3C6904C0 Content-Location: file:///C:/E51446F3/1Exponents_files/slide0127_image025.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHgAEAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAQAa AAIAgAAAAAAAAAIGjI+py70FADs= ------=_NextPart_01C82E61.3C6904C0 Content-Location: file:///C:/E51446F3/1Exponents_files/slide0127_image026.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHgAEAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAb AAIAgAAAAAAAAAIGjI+py90FADs= ------=_NextPart_01C82E61.3C6904C0 Content-Location: file:///C:/E51446F3/1Exponents_files/slide0127_image027.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHgAEAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAb AAIAgAAAAAAAAAIGjI+py90FADs= ------=_NextPart_01C82E61.3C6904C0 Content-Location: file:///C:/E51446F3/1Exponents_files/slide0128.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Exponents
0-power Rule :  A0=3D1 &nb= sp; (A=3D0)
     Reason: 1 =3D      =3D A1–1 =3D A0  =
Negative Power Rule :<= span style=3D'mso-spacerun:yes'>  A-k =3D
     Reason:       =3D=        =3D= A0–k =3D A-k
A<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>1&#= 13;
A<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>1&#= 13;
1<= /div>
A<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>k&#= 13;
1<= /div>
A<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>k&#= 13;
A<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>0&#= 13;
A<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>k&#= 13;
Example B:
Special Exponent= s
b. (2-1 + 3-1)= -2 =3D
a. (2-1 * 3-1)= -2 =3D
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0-power Rule :  A0=3D1 &nb= sp; (A=3D0)
     Reason: 1 =3D      =3D A1–1 =3D A0  =
Negative Power Rule :<= span style=3D'mso-spacerun:yes'>  A-k =3D
     Reason:       =3D=        =3D= A0–k =3D A-k
A<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>1&#= 13;
A<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>1&#= 13;
1<= /div>
A<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>k&#= 13;
1<= /div>
A<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>k&#= 13;
A<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>0&#= 13;
A<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>k&#= 13;
Example B:
Special Exponent= s
b. (2-1 + 3-1)= -2 =3D
a. (2-1 * 3-1)= -2 =3D 22*3= 2 =3D 36
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0-power Rule :  A0=3D1 &nb= sp; (A=3D0)
     Reason: 1 =3D      =3D A1–1 =3D A0  =
Negative Power Rule :<= span style=3D'mso-spacerun:yes'>  A-k =3D
     Reason:       =3D=        =3D= A0–k =3D A-k
A<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>1&#= 13;
A<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>1&#= 13;
1<= /div>
A<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>k&#= 13;
1<= /div>
A<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>k&#= 13;
A<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>0&#= 13;
A<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>k&#= 13;
Example B:
1
3
Special Exponent= s
1
2
(
+
)-2
b. (2-1 + 3-1)= -2 =3D
a. (2-1 * 3-1)= -2 =3D 22*3= 2 =3D 36
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0-power Rule :  A0=3D1 &nb= sp; (A=3D0)
     Reason: 1 =3D      =3D A1–1 =3D A0  =
Negative Power Rule :<= span style=3D'mso-spacerun:yes'>  A-k =3D
     Reason:       =3D=        =3D= A0–k =3D A-k
A<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>1&#= 13;
A<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>1&#= 13;
1<= /div>
A<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>k&#= 13;
1<= /div>
A<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>k&#= 13;
A<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>0&#= 13;
A<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>k&#= 13;
Example B:
1
3
Special Exponent= s
1
2
(
+
)-2
b. (2-1 + 3-1)= -2 =3D
a. (2-1 * 3-1)= -2 =3D 22*3= 2 =3D 36
Note that= = 3;
(2= -1 + 3-1)-2 =3D 22 = + 32 
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0-power Rule :  A0=3D1 &nb= sp; (A=3D0)
     Reason: 1 =3D      =3D A1–1 =3D A0  =
Negative Power Rule :<= span style=3D'mso-spacerun:yes'>  A-k =3D
     Reason:       =3D=        =3D= A0–k =3D A-k
A<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>1&#= 13;
A<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>1&#= 13;
1<= /div>
A<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>k&#= 13;
1<= /div>
A<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>k&#= 13;
A<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>0&#= 13;
A<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>k&#= 13;
Example B:
1
3
Special Exponent= s
1
2
(
+
)-2
b. (2-1 + 3-1)= -2 =3D
a. (2-1 * 3-1)= -2 =3D 22*3= 2 =3D 36
=3D
Note that= = 3;
(2= -1 + 3-1)-2 =3D 22 = + 32 
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0-power Rule :  A0=3D1 &nb= sp; (A=3D0)
     Reason: 1 =3D      =3D A1–1 =3D A0  =
Negative Power Rule :<= span style=3D'mso-spacerun:yes'>  A-k =3D
     Reason:       =3D=        =3D= A0–k =3D A-k
A<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>1&#= 13;
A<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>1&#= 13;
1<= /div>
A<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>k&#= 13;
1<= /div>
A<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>k&#= 13;
A<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>0&#= 13;
A<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>k&#= 13;
Example B:
1
3
5
6
Special Exponent= s
1
2
(
+
)-2
b. (2-1 + 3-1)= -2 =3D
a. (2-1 * 3-1)= -2 =3D 22*3= 2 =3D 36
=3D
(
)-2
Note that= = 3;
(2= -1 + 3-1)-2 =3D 22 = + 32 
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0-power Rule :  A0=3D1 &nb= sp; (A=3D0)
     Reason: 1 =3D      =3D A1–1 =3D A0  =
Negative Power Rule :<= span style=3D'mso-spacerun:yes'>  A-k =3D
     Reason:       =3D=        =3D= A0–k =3D A-k
A<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>1&#= 13;
A<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>1&#= 13;
1<= /div>
A<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>k&#= 13;
1<= /div>
A<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>k&#= 13;
A<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>0&#= 13;
A<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>k&#= 13;
Example B:
1
3
5
6
Special Exponent= s
1
2
(
+
)-2
b. (2-1 + 3-1)= -2 =3D
a. (2-1 * 3-1)= -2 =3D 22*3= 2 =3D 36
=3D
(
)-2
=3D
6
5
(
)2
Note that= = 3;
(2= -1 + 3-1)-2 =3D 22 = + 32 
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0-power Rule :  A0=3D1 &nb= sp; (A=3D0)
     Reason: 1 =3D      =3D A1–1 =3D A0  =
Negative Power Rule :<= span style=3D'mso-spacerun:yes'>  A-k =3D
     Reason:       =3D=        =3D= A0–k =3D A-k
A<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>1&#= 13;
A<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>1&#= 13;
1<= /div>
A<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>k&#= 13;
1<= /div>
A<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>k&#= 13;
A<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>0&#= 13;
A<= span lang=3DEN-US style=3D'font-size:103%;position:relative;top:-.45em;mso-text= -raise: 30%;mso-fareast-language:ZH-CN'>k&#= 13;
Example B:
1
3
5
6
Special Exponent= s
1
2
(
+
)-2
b. (2-1 + 3-1)= -2 =3D
a. (2-1 * 3-1)= -2 =3D 22*3= 2 =3D 36
=3D
(
)-2
=3D
6
5
(
)2
=3D
36
25
Note that= = 3;
(2= -1 + 3-1)-2 =3D 22 = + 32 
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½ = - Power Rule:  A½ =3D &Ou= ml;A<= span lang=3DEN-US style=3D'font-size:156%;color:#FF6600;mso-fareast-language:ZH= -CN; mso-special-format:lastCR;display:none'>
Fractiona= l Powers
------=_NextPart_01C82E61.3C6904C0 Content-Location: file:///C:/E51446F3/1Exponents_files/slide0079_image091.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhBAEdAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAAAD ARwAgAAAAAAAAAKjjI+py+0Po5y02ouzXqD7D4biSJbmiabqyrbuC8efIdf2jef6zqd0DwwKh8Si 6WdMKpdMlwWFbEqn1Gotas1qt1os9wsOB73isvnMIqPX7La6DY9/3/K6vUm/6/fjAP8PKJQXSFio MmiYqAiCuOho2Pgo+Rc5aWlXeanp5rfpCZj5KQoWOmqaVXqqKpW66prU+ior2Dlri7qRq7vL2+v7 C0xRAAA7 ------=_NextPart_01C82E61.3C6904C0 Content-Location: file:///C:/E51446F3/1Exponents_files/slide0136.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Exponents
½ = - Power Rule:  A½ =3D &Ou= ml;A<= span lang=3DEN-US style=3D'font-size:156%;color:#FF6600;mso-fareast-language:ZH= -CN; mso-special-format:lastCR;display:none'>
Fractiona= l Powers
Reason: (= A½)2 = =3D A
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½ = - Power Rule:  A½ =3D &Ou= ml;A<= span lang=3DEN-US style=3D'font-size:156%;color:#FF6600;mso-fareast-language:ZH= -CN; mso-special-format:lastCR;display:none'>
Fractiona= l Powers
Reason: (= A½)2 = =3D A =3D (ÖA)2,
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½ = - Power Rule:  A½ =3D &Ou= ml;A<= span lang=3DEN-US style=3D'font-size:156%;color:#FF6600;mso-fareast-language:ZH= -CN; mso-special-format:lastCR;display:none'>
Fractiona= l Powers
Reason: (= A½)2 = =3D A =3D (ÖA)2, hence A½<= span lang=3DEN-US style=3D'font-size:156%;mso-fareast-language:ZH-CN'> =3D ÖA
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Example C:
= a.16½ =3D
½ = - Power Rule:  A½ =3D &Ou= ml;A<= span lang=3DEN-US style=3D'font-size:156%;color:#FF6600;mso-fareast-language:ZH= -CN; mso-special-format:lastCR;display:none'>
Fractiona= l Powers
Reason: (= A½)2 = =3D A =3D (ÖA)2, hence A½<= span lang=3DEN-US style=3D'font-size:156%;mso-fareast-language:ZH-CN'> =3D ÖA
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Example C:
= a.16½ =3D Ö16 =3D 4= 3;
½ = - Power Rule:  A½ =3D &Ou= ml;A<= span lang=3DEN-US style=3D'font-size:156%;color:#FF6600;mso-fareast-language:ZH= -CN; mso-special-format:lastCR;display:none'>
Fractiona= l Powers
Reason: (= A½)2 = =3D A =3D (ÖA)2, hence A½<= span lang=3DEN-US style=3D'font-size:156%;mso-fareast-language:ZH-CN'> =3D ÖA
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Example C:
= a.16½ =3D Ö16 =3D 4
b.  43/2 =3D
½ = - Power Rule:  A½ =3D &Ou= ml;A<= span lang=3DEN-US style=3D'font-size:156%;color:#FF6600;mso-fareast-language:ZH= -CN; mso-special-format:lastCR;display:none'>
Fractiona= l Powers
Reason: (= A½)2 = =3D A =3D (ÖA)2, hence A½<= span lang=3DEN-US style=3D'font-size:156%;mso-fareast-language:ZH-CN'> =3D ÖA
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