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$\sqrt[ \color{#FF6800}{ 9 } ]{ \color{#FF6800}{ - } \color{#FF6800}{ 512 } }$

$ $ Organize the part that can be taken out of the radical sign inside the square root symbol $ $

$\color{#FF6800}{ 2 } \sqrt[ \color{#FF6800}{ 9 } ]{ \color{#FF6800}{ - } \color{#FF6800}{ 1 } }$

$2 \sqrt[ \color{#FF6800}{ 9 } ]{ \color{#FF6800}{ - } \color{#FF6800}{ 1 } }$

$ $ Move the (-) sign forward $ $

$2 \times \left ( \color{#FF6800}{ - } \sqrt[ \color{#FF6800}{ 9 } ]{ \color{#FF6800}{ 1 } } \right )$

$\color{#FF6800}{ 2 } \color{#FF6800}{ \times } \left ( \color{#FF6800}{ - } \sqrt[ \color{#FF6800}{ 9 } ]{ \color{#FF6800}{ 1 } } \right )$

$ $ Simplify the expression $ $

$\color{#FF6800}{ - } \color{#FF6800}{ 2 }$