What is \sqrt[4]{\sqrt[3]{27x^3}} ?

The solution to \sqrt[4]{\sqrt[3]{27x^3}} is \sqrt[4]{3}\sqrt[12]{x^3}

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simplify \sqrt[4]{\sqrt[3]{27x^3}}

simplify

Solution steps

Apply radical rule:

= ((27 x^{3})^{\frac{1}{3}})^{\frac{1}{4}}

Apply exponent rule:

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

assuming

a \geq 0

= (27 x^{3})^{\frac{1}{3} \cdot \frac{1}{4}}

\frac{1}{3} \cdot \frac{1}{4} = \frac{1}{12}

= (27 x^{3})^{\frac{1}{12}}

Apply radical rule:

assuming

a \geq 0, b \geq 0

- 5 x^{2} y^{2} z^{3}

e^{- 2 (\frac{1}{2})}

\frac{5 ^{n}}{3 ^{n}}

\frac{x + 5}{x - 5}

- 2 e^{- 0.5}

What is \sqrt[4]{\sqrt[3]{27x^3}} ?
The solution to \sqrt[4]{\sqrt[3]{27x^3}} is \sqrt[4]{3}\sqrt[12]{x^3}