What is \sqrt[5]{\sqrt[4]{5x}} ?

The solution to \sqrt[5]{\sqrt[4]{5x}} is \sqrt[20]{5}\sqrt[20]{x}

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simplify \sqrt[5]{\sqrt[4]{5x}}

simplify

Solution steps

Apply radical rule:

= ((5 x)^{\frac{1}{4}})^{\frac{1}{5}}

Apply exponent rule:

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

assuming

a \geq 0

= (5 x)^{\frac{1}{4} \cdot \frac{1}{5}}

\frac{1}{4} \cdot \frac{1}{5} = \frac{1}{20}

= (5 x)^{\frac{1}{20}}

Apply radical rule:

assuming

a \geq 0, b \geq 0

- 2 x (2 x)

ln (x + 2) + ln (x - 2) - 3 ln (x)

ln (\frac{x}{x - 2})

ln (x) - 3 ln (z) + 12 ln (y)

2 ln (\frac{5 e}{3})

What is \sqrt[5]{\sqrt[4]{5x}} ?
The solution to \sqrt[5]{\sqrt[4]{5x}} is \sqrt[20]{5}\sqrt[20]{x}