What is \sqrt[5]{(2\sqrt[13]{4})^2} ?

The solution to \sqrt[5]{(2\sqrt[13]{4})^2} is 2^{6/13}

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simplify \sqrt[5]{(2\sqrt[13]{4})^2}

simplify

2^{\frac{6}{13}}

Decimal Notation

1.37700 \dots

Solution steps

Apply radical rule:

Apply exponent rule:

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

2 \cdot \frac{1}{5} = \frac{2}{5}

Apply exponent rule:

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

= 2^{\frac{2}{5}} \cdot 4^{\frac{2}{65}}

Factor integer

4 = 2^{2}

= 2^{\frac{2}{5}} (2^{2})^{\frac{2}{65}}

Apply exponent rule:

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

(2^{2})^{\frac{2}{65}} = 2^{2 \cdot \frac{2}{65}}

= 2^{\frac{2}{5}} \cdot 2^{2 \cdot \frac{2}{65}}

Refine

= 2^{\frac{2}{5}} \cdot 2^{\frac{4}{65}}

Apply exponent rule:

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

2^{\frac{2}{5}} \cdot 2^{\frac{4}{65}} = 2^{\frac{2}{5} + \frac{4}{65}}

= 2^{\frac{2}{5} + \frac{4}{65}}

Join

\frac{2}{5} + \frac{4}{65} : \frac{6}{13}

= 2^{\frac{6}{13}}

2 e f^{- 1}

(9.6 x 1 0^{- 1}) (5.2 x 1 0^{2})

55 \cdot x x

What is \sqrt[5]{(2\sqrt[13]{4})^2} ?
The solution to \sqrt[5]{(2\sqrt[13]{4})^2} is 2^{6/13}