Simplify ( square root of cube root of 2)^4

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

Rewrite $\sqrt{\sqrt[3]{2}}$ as $\sqrt[6]{2}$ .

${\sqrt[6]{2}}^{4}$

Rewrite ${\sqrt[6]{2}}^{4}$ as ${(2^{4})}^{\frac{1}{6}}$ .

$\sqrt[6]{2^{4}}$

Raise $2$ to the power of $4$ .

$\sqrt[6]{16}$

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

$\sqrt[6]{4^{2}}$

Rewrite $\sqrt[6]{4^{2}}$ as $\sqrt[3]{\sqrt{4^{2}}}$ .

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

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

$\sqrt[3]{4}$

The result can be shown in multiple forms.

Exact Form:

$\sqrt[3]{4}$

Decimal Form:

$1.58740105 \dots$