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Answer
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$3x ^{ 2 } y \div \left( -4xy ^{ 3 } \right) \times 2x ^{ 5 } y ^{ 2 }$
$- \dfrac { 3 x ^ { 6 } } { 2 }$
Arrange the rational expression
$3 \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 5 } } y \div \left ( - 4 x y ^ { 3 } \right ) \times 2 y ^ { 2 }$
$ $ Add the exponent as the base is the same $ $
$3 \color{#FF6800}{ x } ^ { \color{#FF6800}{ 2 } \color{#FF6800}{ + } \color{#FF6800}{ 5 } } y \div \left ( - 4 x y ^ { 3 } \right ) \times 2 y ^ { 2 }$
$3 x ^ { \color{#FF6800}{ 2 } \color{#FF6800}{ + } \color{#FF6800}{ 5 } } y \div \left ( - 4 x y ^ { 3 } \right ) \times 2 y ^ { 2 }$
$ $ Add $ 2 $ and $ 5$
$3 x ^ { \color{#FF6800}{ 7 } } y \div \left ( - 4 x y ^ { 3 } \right ) \times 2 y ^ { 2 }$
$3 x ^ { 7 } \color{#FF6800}{ y } y ^ { 2 } \div \left ( - 4 x y ^ { 3 } \right ) \times 2$
$ $ If the exponent is omitted, the exponent of that term is equal to 1 $ $
$3 x ^ { 7 } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 1 } } y ^ { 2 } \div \left ( - 4 x y ^ { 3 } \right ) \times 2$
$3 x ^ { 7 } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 1 } } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 2 } } \div \left ( - 4 x y ^ { 3 } \right ) \times 2$
$ $ Add the exponent as the base is the same $ $
$3 x ^ { 7 } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 2 } } \div \left ( - 4 x y ^ { 3 } \right ) \times 2$
$3 x ^ { 7 } y ^ { \color{#FF6800}{ 1 } \color{#FF6800}{ + } \color{#FF6800}{ 2 } } \div \left ( - 4 x y ^ { 3 } \right ) \times 2$
$ $ Add $ 1 $ and $ 2$
$3 x ^ { 7 } y ^ { \color{#FF6800}{ 3 } } \div \left ( - 4 x y ^ { 3 } \right ) \times 2$
$\color{#FF6800}{ 3 } \color{#FF6800}{ x } ^ { \color{#FF6800}{ 7 } } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 3 } } \color{#FF6800}{ \div } \left ( \color{#FF6800}{ - } \color{#FF6800}{ 4 } \color{#FF6800}{ x } \color{#FF6800}{ y } ^ { \color{#FF6800}{ 3 } } \right ) \color{#FF6800}{ \times } \color{#FF6800}{ 2 }$
$ $ Calculate the multiplication expression $ $
$\color{#FF6800}{ - } \color{#FF6800}{ \dfrac { 3 x ^ { 6 } } { 2 } }$
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