Question

Please help with this problem. I keep getting -25

Answer 1

$\bf -\sqrt[5]{-(400^2)}\implies -\sqrt[5]{-[(20\cdot 20)^2]}\implies -\sqrt[5]{-[(20^2)^2]} \\\\\\ -\sqrt[5]{-(20^{2\cdot 2})}\implies -\sqrt[5]{-(20)^4}\implies -\sqrt[5]{-(2^2\cdot 5)^4} \\\\\\ -\sqrt[5]{-2^{2\cdot 4}\cdot 5^4}\implies -\sqrt[5]{-2^8\cdot 5^4}\implies -\sqrt[5]{-2^{5+3}\cdot 5^4} \\\\\\ -\sqrt[5]{-2^5\cdot 2^3\cdot 5^4}\implies 2\sqrt[5]{2^3\cdot 5^4}\implies 2\sqrt[5]{5000}$