What is sqrt(\sqrt[4]{(1/x)^{-2)}} ?

The solution to sqrt(\sqrt[4]{(1/x)^{-2)}} is \sqrt[4]{x}

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simplify sqrt(\sqrt[4]{(1/x)^{-2)}}

simplify

Solution steps

= (\frac{1}{x})^{- \frac{1}{2}}

(\frac{1}{x})^{- \frac{1}{2}} = x

= x

Apply radical rule:

a = a^{\frac{1}{2}}

= (x^{\frac{1}{2}})^{\frac{1}{2}}

Apply exponent rule:

(a^{b})^{c} = a^{b c},

assuming

a \geq 0

= x^{\frac{1}{2} \cdot \frac{1}{2}}

\frac{1}{2} \cdot \frac{1}{2} = \frac{1}{4}

= x^{\frac{1}{4}}

\frac{81}{256}

\frac{x ^{x}}{( x + 1 ) ^{x}}

9 \cdot 1 0^{- 9}

- 2 x y^{2} (5 x y^{2})

(- 25)^{- \frac{3}{2}}

What is sqrt(\sqrt[4]{(1/x)^{-2)}} ?
The solution to sqrt(\sqrt[4]{(1/x)^{-2)}} is \sqrt[4]{x}