What is \sqrt[3]{sqrt(\sqrt{5^{24)}}} ?

The solution to \sqrt[3]{sqrt(\sqrt{5^{24)}}} is 25

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simplify \sqrt[3]{sqrt(\sqrt{5^{24)}}}

simplify

3 5^{24}

25

Solution steps

3 5^{24}

5^{24} = 15625

= 315625

Factor the number:

15625 = 2 5^{3}

= 3 2 5^{3}

Apply radical rule:

n a^{n} = a, a \geq 0

3 2 5^{3} = 25

= 25

\frac{1}{2} \cdot \frac{2}{2}

2^{9}

\frac{3 4}{3 9}

(1 + x)^{- \frac{1}{5}}

(3 x^{5} y) (4 x^{6} y^{6} z^{6})

What is \sqrt[3]{sqrt(\sqrt{5^{24)}}} ?
The solution to \sqrt[3]{sqrt(\sqrt{5^{24)}}} is 25