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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
$x ^{ 5 } \div x ^{ 4 }$
$x$
Arrange the rational expression
$x ^ { 5 } \div \color{#FF6800}{ x } ^ { \color{#FF6800}{ 4 } }$
 Convert the division to multiplication and the exponent to the opposite symbol 
$x ^ { 5 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ - } \color{#FF6800}{ 4 } }$
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 5 } } \color{#FF6800}{ x } ^ { \color{#FF6800}{ - } \color{#FF6800}{ 4 } }$
 Add the exponent as the base is the same 
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 5 } \color{#FF6800}{ - } \color{#FF6800}{ 4 } }$
$x ^ { \color{#FF6800}{ 5 } \color{#FF6800}{ - } \color{#FF6800}{ 4 } }$
 Subtract $4$ from $5$
$x ^ { \color{#FF6800}{ 1 } }$
$x ^ { \color{#FF6800}{ 1 } }$
 If the exponent is 1, get rid of it as it is unnecessary 
$x$
$x$
Organize using the law of exponent
$x ^ { 5 } \div \color{#FF6800}{ x } ^ { \color{#FF6800}{ 4 } }$
 Convert the division to multiplication and the exponent to the opposite symbol 
$x ^ { 5 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ - } \color{#FF6800}{ 4 } }$
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 5 } } \color{#FF6800}{ x } ^ { \color{#FF6800}{ - } \color{#FF6800}{ 4 } }$
 Add the exponent as the base is the same 
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 5 } \color{#FF6800}{ - } \color{#FF6800}{ 4 } }$
$x ^ { \color{#FF6800}{ 5 } \color{#FF6800}{ - } \color{#FF6800}{ 4 } }$
 Subtract $4$ from $5$
$x ^ { \color{#FF6800}{ 1 } }$
$x ^ { \color{#FF6800}{ 1 } }$
 If the exponent is 1, get rid of it as it is unnecessary 
$x$
$x$
Use the synthetic division to find the quotient and the remainder
$x ^ { 5 } \div \color{#FF6800}{ x } ^ { \color{#FF6800}{ 4 } }$
 Convert the division to multiplication and the exponent to the opposite symbol 
$x ^ { 5 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ - } \color{#FF6800}{ 4 } }$
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 5 } } \color{#FF6800}{ x } ^ { \color{#FF6800}{ - } \color{#FF6800}{ 4 } }$
 Add the exponent as the base is the same 
$\color{#FF6800}{ x } ^ { \color{#FF6800}{ 5 } \color{#FF6800}{ - } \color{#FF6800}{ 4 } }$
$x ^ { \color{#FF6800}{ 5 } \color{#FF6800}{ - } \color{#FF6800}{ 4 } }$
 Subtract $4$ from $5$
$x ^ { \color{#FF6800}{ 1 } }$
$x ^ { \color{#FF6800}{ 1 } }$
 If the exponent is 1, get rid of it as it is unnecessary 
$x$
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