What is sqrt(\sqrt{\sqrt{X^5)}} ?

The solution to sqrt(\sqrt{\sqrt{X^5)}} is \sqrt[4]{X^{5/2}}

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simplify sqrt(\sqrt{\sqrt{X^5)}}

simplify

X^{5}

Solution steps

X^{5}

X^{5} : X^{\frac{5}{2}}

= X^{\frac{5}{2}}

Apply radical rule:

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

= ((X^{\frac{5}{2}})^{\frac{1}{2}})^{\frac{1}{2}}

Apply exponent rule:

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

assuming

a \geq 0

= (X^{\frac{5}{2}})^{\frac{1}{2} \cdot \frac{1}{2}}

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

= (X^{\frac{5}{2}})^{\frac{1}{4}}

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

(\frac{3}{2}) \cdot π

(4 x^{2}) \cdot (2 x)

(2^{3})^{4} (3^{2} 0. 2^{3})^{3}

4 x (7 x^{2})

What is sqrt(\sqrt{\sqrt{X^5)}} ?
The solution to sqrt(\sqrt{\sqrt{X^5)}} is \sqrt[4]{X^{5/2}}