What is \sqrt[5]{\sqrt[4]{\sqrt[3]{16^6}}} ?

The solution to \sqrt[5]{\sqrt[4]{\sqrt[3]{16^6}}} is \sqrt[20]{256}

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simplify \sqrt[5]{\sqrt[4]{\sqrt[3]{16^6}}}

simplify

Decimal Notation

1.31950 \dots

Solution steps

Apply radical rule:

= ((1 6^{2})^{\frac{1}{4}})^{\frac{1}{5}}

Apply exponent rule:

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

= (1 6^{2})^{\frac{1}{4} \cdot \frac{1}{5}}

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

= (1 6^{2})^{\frac{1}{20}}

1 6^{2} = 256

x^{3} e^{- x^{2}}

(- 256 x^{5} y^{4}) e n t re (- 16 x^{8} y^{9})

e^{- l n ∣ y ∣}

- 14 x^{3} y^{3} (16 x^{3})

f (x) = \frac{e ^{- x}}{e ^{- 2 x}}

What is \sqrt[5]{\sqrt[4]{\sqrt[3]{16^6}}} ?
The solution to \sqrt[5]{\sqrt[4]{\sqrt[3]{16^6}}} is \sqrt[20]{256}