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Calculate the value
Answer
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$\left( 2 ^{ \frac{ 1 }{ 4 } } +2 ^{ - \frac{ 1 }{ 4 } } \right) ^{ 2 }$
$\dfrac { 4 + 3 \sqrt{ 2 } } { 2 }$
Calculate the value
$\left ( \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ \frac { 1 } { 4 } } } + 2 ^ { - \frac { 1 } { 4 } } \right ) ^ { 2 }$
$ $ Calculate power $ $
$\left ( \sqrt[ \color{#FF6800}{ 4 } ]{ \color{#FF6800}{ 2 } } + 2 ^ { - \frac { 1 } { 4 } } \right ) ^ { 2 }$
$\left ( \sqrt[ 4 ]{ 2 } + 2 ^ { \color{#FF6800}{ - } \color{#FF6800}{ \frac { 1 } { 4 } } } \right ) ^ { 2 }$
$ $ If the exponent is negative, change it to a fraction $ $
$\left ( \sqrt[ 4 ]{ 2 } + \dfrac { 1 } { 2 ^ { \frac { 1 } { 4 } } } \right ) ^ { 2 }$
$\left ( \sqrt[ 4 ]{ 2 } + \dfrac { 1 } { \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ \frac { 1 } { 4 } } } } \right ) ^ { 2 }$
$ $ Calculate power $ $
$\left ( \sqrt[ 4 ]{ 2 } + \dfrac { 1 } { \sqrt[ \color{#FF6800}{ 4 } ]{ \color{#FF6800}{ 2 } } } \right ) ^ { 2 }$
$\left ( \sqrt[ 4 ]{ 2 } + \color{#FF6800}{ \dfrac { 1 } { \sqrt[ 4 ]{ 2 } } } \right ) ^ { 2 }$
$ $ Calculate the expression $ $
$\left ( \sqrt[ 4 ]{ 2 } + \color{#FF6800}{ \dfrac { \left ( \sqrt[ 4 ]{ 2 } \right ) ^ { 3 } } { 2 } } \right ) ^ { 2 }$
$\left ( \sqrt[ 4 ]{ 2 } + \dfrac { \left ( \sqrt[ \color{#FF6800}{ 4 } ]{ \color{#FF6800}{ 2 } } \right ) ^ { \color{#FF6800}{ 3 } } } { 2 } \right ) ^ { 2 }$
$ $ Calculate power $ $
$\left ( \sqrt[ 4 ]{ 2 } + \dfrac { \sqrt[ \color{#FF6800}{ 4 } ]{ \color{#FF6800}{ 8 } } } { 2 } \right ) ^ { 2 }$
$\left ( \sqrt[ \color{#FF6800}{ 4 } ]{ \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \color{#FF6800}{ \dfrac { \sqrt[ 4 ]{ 8 } } { 2 } } \right ) ^ { 2 }$
$ $ Find the sum of the fractions $ $
$\left ( \color{#FF6800}{ \dfrac { 2 \sqrt[ 4 ]{ 2 } + \sqrt[ 4 ]{ 8 } } { 2 } } \right ) ^ { 2 }$
$\left ( \color{#FF6800}{ \dfrac { 2 \sqrt[ 4 ]{ 2 } + \sqrt[ 4 ]{ 8 } } { 2 } } \right ) ^ { \color{#FF6800}{ 2 } }$
$ $ When raising a fraction to the power, raise the numerator and denominator each to the power $ $
$\dfrac { \left ( \color{#FF6800}{ 2 } \sqrt[ \color{#FF6800}{ 4 } ]{ \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \sqrt[ \color{#FF6800}{ 4 } ]{ \color{#FF6800}{ 8 } } \right ) ^ { \color{#FF6800}{ 2 } } } { \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 2 } } }$
$\dfrac { \left ( \color{#FF6800}{ 2 } \sqrt[ \color{#FF6800}{ 4 } ]{ \color{#FF6800}{ 2 } } \color{#FF6800}{ + } \sqrt[ \color{#FF6800}{ 4 } ]{ \color{#FF6800}{ 8 } } \right ) ^ { \color{#FF6800}{ 2 } } } { 2 ^ { 2 } }$
$ $ Calculate power $ $
$\dfrac { \color{#FF6800}{ 8 } \color{#FF6800}{ + } \color{#FF6800}{ 6 } \sqrt{ \color{#FF6800}{ 2 } } } { 2 ^ { 2 } }$
$\dfrac { 8 + 6 \sqrt{ 2 } } { \color{#FF6800}{ 2 } ^ { \color{#FF6800}{ 2 } } }$
$ $ Calculate power $ $
$\dfrac { 8 + 6 \sqrt{ 2 } } { \color{#FF6800}{ 4 } }$
$\color{#FF6800}{ \dfrac { 8 + 6 \sqrt{ 2 } } { 4 } }$
$ $ Reduce the fraction $ $
$\color{#FF6800}{ \dfrac { 4 + 3 \sqrt{ 2 } } { 2 } }$
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