What is \sqrt[7]{20/13}^{2.5} ?

The solution to \sqrt[7]{20/13}^{2.5} is 1.16631…

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simplify \sqrt[7]{20/13}^{2.5}

simplify

1.16631 \dots

Solution steps

Apply radical rule:

= ((\frac{20}{13})^{\frac{1}{7}})^{2.5}

Apply exponent rule:

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

= (\frac{20}{13})^{\frac{1}{7} \cdot 2.5}

\frac{1}{7} \cdot 2.5 = 0.35714 \dots

= (\frac{20}{13})^{0.35714 \dots}

Convert element to a decimal form

\frac{20}{13} = 1.53846 \dots

= 1.53846 \dots^{0.35714 \dots}

1.53846 \dots^{0.35714 \dots} = 1.16631 \dots

= 1.16631 \dots

\frac{1}{100} \cdot (2.31 \cdot 1 0^{- 20})

(8.7 \cdot 1 0^{4}) \cdot (10 \cdot 1 0^{- 2} \cdot 30 \cdot 1 0^{- 2})

- 36312 \cdot e^{- 534 \cdot 4}

What is \sqrt[7]{20/13}^{2.5} ?
The solution to \sqrt[7]{20/13}^{2.5} is 1.16631…