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$4xy \div \left( -3xy \right) ^{ 2 } \times \dfrac{ 3 }{ 8 } xy ^{ 2 }$
$\dfrac { y } { 6 }$
Arrange the rational expression
$4 \color{#FF6800}{ x } x y \div \left ( - 3 x y \right ) ^ { 2 } \times \dfrac { 3 } { 8 } y ^ { 2 }$
$ $ If the exponent is omitted, the exponent of that term is equal to 1 $ $
$4 \color{#FF6800}{ x } ^ { \color{#FF6800}{ 1 } } x y \div \left ( - 3 x y \right ) ^ { 2 } \times \dfrac { 3 } { 8 } y ^ { 2 }$
$4 x ^ { 1 } \color{#FF6800}{ x } y \div \left ( - 3 x y \right ) ^ { 2 } \times \dfrac { 3 } { 8 } y ^ { 2 }$
$ $ If the exponent is omitted, the exponent of that term is equal to 1 $ $
$4 x ^ { 1 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 1 } } y \div \left ( - 3 x y \right ) ^ { 2 } \times \dfrac { 3 } { 8 } y ^ { 2 }$
$4 \color{#FF6800}{ x } ^ { \color{#FF6800}{ 1 } } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 1 } } y \div \left ( - 3 x y \right ) ^ { 2 } \times \dfrac { 3 } { 8 } y ^ { 2 }$
$ $ Add the exponent as the base is the same $ $
$4 \color{#FF6800}{ x } ^ { \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } } y \div \left ( - 3 x y \right ) ^ { 2 } \times \dfrac { 3 } { 8 } y ^ { 2 }$
$4 x ^ { \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 1 } } y \div \left ( - 3 x y \right ) ^ { 2 } \times \dfrac { 3 } { 8 } y ^ { 2 }$
$ $ Add $ 1 $ and $ 1$
$4 x ^ { \color{#FF6800}{ 2 } } y \div \left ( - 3 x y \right ) ^ { 2 } \times \dfrac { 3 } { 8 } y ^ { 2 }$
$4 x ^ { 2 } \color{#FF6800}{ y } y ^ { 2 } \div \left ( - 3 x y \right ) ^ { 2 } \times \dfrac { 3 } { 8 }$
$ $ If the exponent is omitted, the exponent of that term is equal to 1 $ $
$4 x ^ { 2 } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 1 } } y ^ { 2 } \div \left ( - 3 x y \right ) ^ { 2 } \times \dfrac { 3 } { 8 }$
$4 x ^ { 2 } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 1 } } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 2 } } \div \left ( - 3 x y \right ) ^ { 2 } \times \dfrac { 3 } { 8 }$
$ $ Add the exponent as the base is the same $ $
$4 x ^ { 2 } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 2 } } \div \left ( - 3 x y \right ) ^ { 2 } \times \dfrac { 3 } { 8 }$
$4 x ^ { 2 } y ^ { \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 2 } } \div \left ( - 3 x y \right ) ^ { 2 } \times \dfrac { 3 } { 8 }$
$ $ Add $ 1 $ and $ 2$
$4 x ^ { 2 } y ^ { \color{#FF6800}{ 3 } } \div \left ( - 3 x y \right ) ^ { 2 } \times \dfrac { 3 } { 8 }$
$\color{#FF6800}{ 4 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ \div } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 3 } \color{#FF6800}{ x } \color{#FF6800}{ y } \right ) ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { 3 } { 8 } }$
$ $ Calculate the multiplication expression $ $
$\color{#FF6800}{ \dfrac { y } { 6 } }$
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