What is (\sqrt[7]{7sqrt(7\sqrt{7)}})^2 ?

The solution to (\sqrt[7]{7sqrt(7\sqrt{7)}})^2 is square root of 7

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simplify (\sqrt[7]{7sqrt(7\sqrt{7)}})^2

simplify

7

Decimal Notation

2.64575 \dots

Solution steps

Apply radical rule:

= ((777)^{\frac{1}{7}})^{2}

Apply exponent rule:

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

= (777)^{\frac{1}{7} \cdot 2}

\frac{1}{7} \cdot 2 = \frac{2}{7}

= (777)^{\frac{2}{7}}

77 = 7^{\frac{3}{4}}

= (7 \cdot 7^{\frac{3}{4}})^{\frac{2}{7}}

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

= 7^{\frac{2}{7}} (7^{\frac{3}{4}})^{\frac{2}{7}}

(7^{\frac{3}{4}})^{\frac{2}{7}} : 7^{\frac{3}{14}}

= 7^{\frac{2}{7}} \cdot 7^{\frac{3}{14}}

Apply exponent rule:

a^{b} \cdot a^{c} = a^{b + c}

7^{\frac{2}{7}} \cdot 7^{\frac{3}{14}} = 7^{\frac{2}{7} + \frac{3}{14}}

= 7^{\frac{2}{7} + \frac{3}{14}}

Join

\frac{2}{7} + \frac{3}{14} : \frac{1}{2}

= 7

\frac{x + x + x}{x + 1}

e^{- t} sin (h) (5 t)

What is (\sqrt[7]{7sqrt(7\sqrt{7)}})^2 ?
The solution to (\sqrt[7]{7sqrt(7\sqrt{7)}})^2 is square root of 7