What is \sqrt[4]{\sqrt[5]{81}} ?

The solution to \sqrt[4]{\sqrt[5]{81}} is \sqrt[5]{3}

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simplify \sqrt[4]{\sqrt[5]{81}}

simplify

Decimal Notation

1.24573 \dots

Solution steps

Apply radical rule:

= (8 1^{\frac{1}{5}})^{\frac{1}{4}}

Apply exponent rule:

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

= 8 1^{\frac{1}{5} \cdot \frac{1}{4}}

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

= 8 1^{\frac{1}{20}}

Factor the number:

81 = 3^{4}

Apply exponent rule:

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

120000 e^{- 0.05 (10)}

0.16875 \cdot 1 0^{- 1}

a b \cdot b a

e^{- \frac{8760}{13140}}

What is \sqrt[4]{\sqrt[5]{81}} ?
The solution to \sqrt[4]{\sqrt[5]{81}} is \sqrt[5]{3}