Simplify the Radical Expression cube root of square root of 64a^10b^34

$\sqrt[3]{\sqrt{64 a^{10} b^{34}}}$

Rewrite $64 a^{10} b^{34}$ as ${(8 a^{5} b^{17})}^{2}$ .

$\sqrt[3]{\sqrt{{(8 a^{5} b^{17})}^{2}}}$

Pull terms out from under the radical.

$\sqrt[3]{| 8 a^{5} b^{17} |}$

Remove non-negative terms from the absolute value.

$\sqrt[3]{8 | a^{5} b^{17} |}$

Rewrite $8$ as $2^{3}$ .

$\sqrt[3]{2^{3} | a^{5} b^{17} |}$

Pull terms out from under the radical.

$2 \sqrt[3]{| a^{5} b^{17} |}$