What is \sqrt[6]{\sqrt[3]{sqrt(8^6)}} ?

The solution to \sqrt[6]{\sqrt[3]{sqrt(8^6)}} is square root of 2

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simplify \sqrt[6]{\sqrt[3]{sqrt(8^6)}}

simplify

2

Solution steps

8^{6} : 8^{3}

Apply radical rule:

= ((8^{3})^{\frac{1}{3}})^{\frac{1}{6}}

Apply exponent rule:

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

= (8^{3})^{\frac{1}{3} \cdot \frac{1}{6}}

\frac{1}{3} \cdot \frac{1}{6} = \frac{1}{18}

= (8^{3})^{\frac{1}{18}}

8^{3} = 512

Factor the number:

512 = 2^{9}

Apply exponent rule:

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

= 2

What is \sqrt[6]{\sqrt[3]{sqrt(8^6)}} ?
The solution to \sqrt[6]{\sqrt[3]{sqrt(8^6)}} is square root of 2