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

The solution to \sqrt[5]{5^{sqrt(5/4)}} is 5^{1/(2sqrt(5))}

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

simplify

5^{\frac{1}{2 5}}

Solution steps

Apply radical rule:

= (5^{\frac{5}{4}})^{\frac{1}{5}}

Apply exponent rule:

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

= 5^{\frac{5}{4} \frac{1}{5}}

\frac{5}{4} \frac{1}{5} = \frac{1}{2 5}

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

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

e^{- a ∣ x ∣}

\frac{e ^{5 x}}{e ^{3 x}}

\frac{2.7}{7.5}

(30 x^{4}) (7 x^{5} y)

15000 e^{- 0.03 x}

What is \sqrt[5]{5^{sqrt(5/4)}} ?
The solution to \sqrt[5]{5^{sqrt(5/4)}} is 5^{1/(2sqrt(5))}