What is \sqrt[5]{\sqrt[4]{\sqrt[3]{16}}} ?

The solution to \sqrt[5]{\sqrt[4]{\sqrt[3]{16}}} is \sqrt[15]{2}

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simplify \sqrt[5]{\sqrt[4]{\sqrt[3]{16}}}

simplify

Decimal Notation

1.04729 \dots

Solution steps

Apply radical rule:

= (1 6^{\frac{1}{12}})^{\frac{1}{5}}

Apply exponent rule:

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

= 1 6^{\frac{1}{12} \cdot \frac{1}{5}}

\frac{1}{12} \cdot \frac{1}{5} = \frac{1}{60}

= 1 6^{\frac{1}{60}}

(2.4 x 1 0^{4}) (4.5 x 1 0^{3})

200 e^{- 0.5 p}

(3 x^{2} y) (7 x y^{4})

V^{1} (3.5) V^{2} (11.5) f^{1} (5.5) f^{2} (9.5)

(x - 2) (4 - x)

What is \sqrt[5]{\sqrt[4]{\sqrt[3]{16}}} ?
The solution to \sqrt[5]{\sqrt[4]{\sqrt[3]{16}}} is \sqrt[15]{2}