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$20$
Calculate the value
$\left ( - 2 \right ) ^ { 3 } \left ( - \dfrac { 5 } { 4 } \right ) ^ { 2 } \times \left ( \color{#FF6800}{ - } \dfrac { 8 } { 5 } \right )$
$ $ Move the (-) sign forward $ $
$\color{#FF6800}{ - } \left ( - 2 \right ) ^ { 3 } \left ( - \dfrac { 5 } { 4 } \right ) ^ { 2 } \times \dfrac { 8 } { 5 }$
$- \left ( \color{#FF6800}{ - } \color{#FF6800}{ 2 } \right ) ^ { \color{#FF6800}{ 3 } } \left ( - \dfrac { 5 } { 4 } \right ) ^ { 2 } \times \dfrac { 8 } { 5 }$
$ $ Move the (-) sign forward as it does not disappear if the (-) sign is powered to an odd number of times $ $
$- \left ( \color{#FF6800}{ - } 2 ^ { 3 } \right ) \left ( - \dfrac { 5 } { 4 } \right ) ^ { 2 } \times \dfrac { 8 } { 5 }$
$\color{#FF6800}{ - } \left ( \color{#FF6800}{ - } 2 ^ { 3 } \right ) \left ( - \dfrac { 5 } { 4 } \right ) ^ { 2 } \times \dfrac { 8 } { 5 }$
$ $ Simplify Minus $ $
$2 ^ { 3 } \left ( - \dfrac { 5 } { 4 } \right ) ^ { 2 } \times \dfrac { 8 } { 5 }$
$\color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 3 } } \left ( - \dfrac { 5 } { 4 } \right ) ^ { 2 } \times \dfrac { 8 } { 5 }$
$ $ Calculate power $ $
$\color{#FF6800}{ 8 } \left ( - \dfrac { 5 } { 4 } \right ) ^ { 2 } \times \dfrac { 8 } { 5 }$
$8 \left ( \color{#FF6800}{ - } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 5 } } { \color{#FF6800}{ 4 } } } \right ) ^ { \color{#FF6800}{ 2 } } \times \dfrac { 8 } { 5 }$
$ $ Remove negative signs because negative numbers raised to even powers are positive $ $
$8 \left ( \dfrac { 5 } { 4 } \right ) ^ { 2 } \times \dfrac { 8 } { 5 }$
$8 \left ( \color{#FF6800}{ \dfrac { \color{#FF6800}{ 5 } } { \color{#FF6800}{ 4 } } } \right ) ^ { \color{#FF6800}{ 2 } } \times \dfrac { 8 } { 5 }$
$ $ When raising a fraction to the power, raise the numerator and denominator each to the power $ $
$8 \times \dfrac { \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 2 } } } { \color{#FF6800}{ 4 } ^ { \color{#FF6800}{ 2 } } } \times \dfrac { 8 } { 5 }$
$8 \times \dfrac { \color{#FF6800}{ 5 } ^ { \color{#FF6800}{ 2 } } } { 4 ^ { 2 } } \times \dfrac { 8 } { 5 }$
$ $ Calculate power $ $
$8 \times \dfrac { \color{#FF6800}{ 25 } } { 4 ^ { 2 } } \times \dfrac { 8 } { 5 }$
$8 \times \dfrac { 25 } { \color{#FF6800}{ 4 } ^ { \color{#FF6800}{ 2 } } } \times \dfrac { 8 } { 5 }$
$ $ Calculate power $ $
$8 \times \dfrac { 25 } { \color{#FF6800}{ 16 } } \times \dfrac { 8 } { 5 }$
$\color{#FF6800}{ 8 } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 25 } } { \color{#FF6800}{ 16 } } } \color{#FF6800}{ \times } \color{#FF6800}{ \dfrac { \color{#FF6800}{ 8 } } { \color{#FF6800}{ 5 } } }$
$ $ Calculate the product of rational numbers $ $
$\color{#FF6800}{ 20 }$
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