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$9$
Calculate the value
$\left ( \color{#FF6800}{ \dfrac { \color{#FF6800}{ 1 } } { \color{#FF6800}{ 3 } } } \right ) ^ { \color{#FF6800}{ - } \color{#FF6800}{ 2 } }$
$ $ When raising a fraction to the power, raise the numerator and denominator each to the power $ $
$\dfrac { \color{#FF6800}{ 1 } ^ { \color{#FF6800}{ - } \color{#FF6800}{ 2 } } } { \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ - } \color{#FF6800}{ 2 } } }$
$\dfrac { 1 ^ { \color{#FF6800}{ - } \color{#FF6800}{ 2 } } } { 3 ^ { - 2 } }$
$ $ If the exponent is negative, change it to a fraction $ $
$\dfrac { \dfrac { 1 } { 1 ^ { 2 } } } { 3 ^ { - 2 } }$
$\color{#FF6800}{ \dfrac { \color{#FF6800}{ \dfrac { \color{#FF6800}{ 1 } } { \color{#FF6800}{ 1 } ^ { \color{#FF6800}{ 2 } } } } } { \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ - } \color{#FF6800}{ 2 } } } }$
$ $ Calculate the complex fraction $ $
$\color{#FF6800}{ \dfrac { \color{#FF6800}{ 1 } } { \color{#FF6800}{ 1 } ^ { \color{#FF6800}{ 2 } } \color{#FF6800}{ \times } \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ - } \color{#FF6800}{ 2 } } } }$
$\dfrac { 1 } { \color{#FF6800}{ 1 } ^ { \color{#FF6800}{ 2 } } \times 3 ^ { - 2 } }$
$ $ Calculate power $ $
$\dfrac { 1 } { \color{#FF6800}{ 1 } \times 3 ^ { - 2 } }$
$\dfrac { 1 } { \color{#FF6800}{ 1 } \times 3 ^ { - 2 } }$
$ $ Multiplying any number by 1 does not change the value $ $
$\dfrac { 1 } { 3 ^ { - 2 } }$
$\dfrac { 1 } { 3 ^ { \color{#FF6800}{ - } \color{#FF6800}{ 2 } } }$
$ $ If the exponent is negative, change it to a fraction $ $
$\dfrac { 1 } { \dfrac { 1 } { 3 ^ { 2 } } }$
$\color{#FF6800}{ \dfrac { \color{#FF6800}{ 1 } } { \color{#FF6800}{ \dfrac { \color{#FF6800}{ 1 } } { \color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 2 } } } } } }$
$ $ Calculate the complex fraction $ $
$\color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 2 } }$
$\color{#FF6800}{ 3 } ^ { \color{#FF6800}{ 2 } }$
$ $ Calculate power $ $
$\color{#FF6800}{ 9 }$
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