Simplify cube root of fourth root of 16

$\sqrt[3]{\sqrt[4]{16}}$

Step 1

Rewrite $16$ as $2^{4}$ .

$\sqrt[3]{\sqrt[4]{2^{4}}}$

Step 2

Pull terms out from under the radical, assuming positive real numbers.

$\sqrt[3]{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\sqrt[3]{2}$

Decimal Form:

$1.25992104 \dots$