What is \sqrt[4]{\sqrt[5]{81b^{10}}} ?

The solution to \sqrt[4]{\sqrt[5]{81b^{10}}} is \sqrt[5]{3}sqrt(b)

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simplify \sqrt[4]{\sqrt[5]{81b^{10}}}

simplify

Solution steps

Apply radical rule:

= ((81 b^{10})^{\frac{1}{5}})^{\frac{1}{4}}

Apply exponent rule:

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

assuming

a \geq 0

= (81 b^{10})^{\frac{1}{5} \cdot \frac{1}{4}}

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

= (81 b^{10})^{\frac{1}{20}}

Apply radical rule:

assuming

a \geq 0, b \geq 0

Apply exponent rule:

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

b^{10} = b^{0.5 \cdot 20} = (b)^{20}

Apply radical rule:

assuming

a \geq 0

(17 \cdot 1 0^{- 3}) (9.8)

e^{- t} \cdot sinh (t)

(X + 1)^{2} \cdot (X - 2)^{2}

90 e^{- \frac{527}{650}}

What is \sqrt[4]{\sqrt[5]{81b^{10}}} ?
The solution to \sqrt[4]{\sqrt[5]{81b^{10}}} is \sqrt[5]{3}sqrt(b)