Question

$(\sqrt[5]{3})^{10}$?

Answer 1

(3^1/5)^10
3^1/5 x 10
3^10/5
3^2 = 9

Answer 2

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

$\sqrt[c]{a^{b}}=a^{b/c}$
______________________

$(\sqrt[5]{3})^{10}=(\sqrt[5]{3^{1}})^{10}\\(\sqrt[5]{3})^{10}=(3^{1/5})^{10}\\(\sqrt[5]{3})^{10}=3^{(1/5).10}\\(\sqrt[5]{3})^{10}=3^{10/5}\\(\sqrt[5]{3})^{10}=3^{2}\\(\sqrt[5]{3})^{10}=9$