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Formula
Calculate the value
Organize using the law of exponent
Use the synthetic division to find the quotient and the remainder
$a ^{ 12 } \div a ^{ 4 }$
$a ^ { 8 }$
Arrange the rational expression
$a ^ { 12 } \div \color{#FF6800}{ a } ^ { \color{#FF6800}{ 4 } }$
 Convert the division to multiplication and the exponent to the opposite symbol 
$a ^ { 12 } \color{#FF6800}{ a } ^ { \color{#FF6800}{ - } \color{#FF6800}{ 4 } }$
$\color{#FF6800}{ a } ^ { \color{#FF6800}{ 12 } } \color{#FF6800}{ a } ^ { \color{#FF6800}{ - } \color{#FF6800}{ 4 } }$
 Add the exponent as the base is the same 
$\color{#FF6800}{ a } ^ { \color{#FF6800}{ 12 } \color{#FF6800}{ - } \color{#FF6800}{ 4 } }$
$a ^ { \color{#FF6800}{ 12 } \color{#FF6800}{ - } \color{#FF6800}{ 4 } }$
 Subtract $4$ from $12$
$a ^ { \color{#FF6800}{ 8 } }$
$a ^ { 8 }$
Organize using the law of exponent
$a ^ { 12 } \div \color{#FF6800}{ a } ^ { \color{#FF6800}{ 4 } }$
 Convert the division to multiplication and the exponent to the opposite symbol 
$a ^ { 12 } \color{#FF6800}{ a } ^ { \color{#FF6800}{ - } \color{#FF6800}{ 4 } }$
$\color{#FF6800}{ a } ^ { \color{#FF6800}{ 12 } } \color{#FF6800}{ a } ^ { \color{#FF6800}{ - } \color{#FF6800}{ 4 } }$
 Add the exponent as the base is the same 
$\color{#FF6800}{ a } ^ { \color{#FF6800}{ 12 } \color{#FF6800}{ - } \color{#FF6800}{ 4 } }$
$a ^ { \color{#FF6800}{ 12 } \color{#FF6800}{ - } \color{#FF6800}{ 4 } }$
 Subtract $4$ from $12$
$a ^ { \color{#FF6800}{ 8 } }$
$a ^ { 8 }$
Use the synthetic division to find the quotient and the remainder
$a ^ { 12 } \div \color{#FF6800}{ a } ^ { \color{#FF6800}{ 4 } }$
 Convert the division to multiplication and the exponent to the opposite symbol 
$a ^ { 12 } \color{#FF6800}{ a } ^ { \color{#FF6800}{ - } \color{#FF6800}{ 4 } }$
$\color{#FF6800}{ a } ^ { \color{#FF6800}{ 12 } } \color{#FF6800}{ a } ^ { \color{#FF6800}{ - } \color{#FF6800}{ 4 } }$
 Add the exponent as the base is the same 
$\color{#FF6800}{ a } ^ { \color{#FF6800}{ 12 } \color{#FF6800}{ - } \color{#FF6800}{ 4 } }$
$a ^ { \color{#FF6800}{ 12 } \color{#FF6800}{ - } \color{#FF6800}{ 4 } }$
 Subtract $4$ from $12$
$a ^ { \color{#FF6800}{ 8 } }$
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