What is \sqrt[7]{\sqrt[7]{x}} ?

The solution to \sqrt[7]{\sqrt[7]{x}} is \sqrt[49]{x}

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simplify \sqrt[7]{\sqrt[7]{x}}

simplify

Solution steps

Apply radical rule:

= (x^{\frac{1}{7}})^{\frac{1}{7}}

Apply exponent rule:

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

assuming

a \geq 0

= x^{\frac{1}{7} \cdot \frac{1}{7}}

\frac{1}{7} \cdot \frac{1}{7} = \frac{1}{49}

= x^{\frac{1}{49}}

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What is \sqrt[7]{\sqrt[7]{x}} ?
The solution to \sqrt[7]{\sqrt[7]{x}} is \sqrt[49]{x}