What is \sqrt[3]{\sqrt[5]{\sqrt[7]{a/(b^2)}}} ?

The solution to \sqrt[3]{\sqrt[5]{\sqrt[7]{a/(b^2)}}} is \sqrt[105]{a/(b^2)}

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simplify \sqrt[3]{\sqrt[5]{\sqrt[7]{a/(b^2)}}}

simplify

Solution steps

Apply radical rule:

= ((\frac{a}{b ^{2}})^{\frac{1}{35}})^{\frac{1}{3}}

Apply exponent rule:

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

assuming

a \geq 0

= (\frac{a}{b ^{2}})^{\frac{1}{35} \cdot \frac{1}{3}}

\frac{1}{35} \cdot \frac{1}{3} = \frac{1}{105}

= (\frac{a}{b ^{2}})^{\frac{1}{105}}

60 (2)^{- 0.02 (405)}

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\frac{- 28}{- 7}

e^{x^{2}} e^{x^{2}}

What is \sqrt[3]{\sqrt[5]{\sqrt[7]{a/(b^2)}}} ?
The solution to \sqrt[3]{\sqrt[5]{\sqrt[7]{a/(b^2)}}} is \sqrt[105]{a/(b^2)}