What is sqrt(\sqrt{x^{-3)+1}} ?

The solution to sqrt(\sqrt{x^{-3)+1}} is \sqrt[4]{(x^3+1)/(x^3)}

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simplify sqrt(\sqrt{x^{-3)+1}}

simplify

x^{- 3} + 1

Solution steps

x^{- 3} + 1

Apply radical rule:

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

= ((x^{- 3} + 1)^{\frac{1}{2}})^{\frac{1}{2}}

Apply exponent rule:

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

assuming

a \geq 0

= (x^{- 3} + 1)^{\frac{1}{2} \cdot \frac{1}{2}}

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

= (x^{- 3} + 1)^{\frac{1}{4}}

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

Join

\frac{1}{x ^{3}} + 1 : \frac{1 + x ^{3}}{x ^{3}}

(p^{4} q^{2}) (p^{7} q^{5})

(3.3 \cdot 1 0^{- 4}) \cdot (8 \cdot 1 0^{0})

t^{2} \cdot e^{- 3 t}

e^{- (\frac{2}{10})^{2}}

e^{- \frac{jπ}{4}}

What is sqrt(\sqrt{x^{-3)+1}} ?
The solution to sqrt(\sqrt{x^{-3)+1}} is \sqrt[4]{(x^3+1)/(x^3)}