Simplify square root of cube root of 1458m^7

$\sqrt{\sqrt[3]{1458 m^{7}}}$

Rewrite $1458 m^{7}$ as ${(9 m^{2})}^{3} \cdot (2 m)$ .

Factor $729$ out of $1458$ .

$\sqrt{\sqrt[3]{729 (2) m^{7}}}$

Rewrite $729$ as $9^{3}$ .

$\sqrt{\sqrt[3]{9^{3} \cdot 2 m^{7}}}$

Factor out $m^{6}$ .

$\sqrt{\sqrt[3]{9^{3} \cdot 2 (m^{6} m)}}$

Rewrite $m^{6}$ as ${(m^{2})}^{3}$ .

$\sqrt{\sqrt[3]{9^{3} \cdot 2 ({(m^{2})}^{3} m)}}$

Move $2$ .

$\sqrt{\sqrt[3]{9^{3} {(m^{2})}^{3} \cdot 2 m}}$

Rewrite $9^{3} {(m^{2})}^{3}$ as ${(9 m^{2})}^{3}$ .

$\sqrt{\sqrt[3]{{(9 m^{2})}^{3} \cdot 2 m}}$

Add parentheses.

$\sqrt{\sqrt[3]{{(9 m^{2})}^{3} \cdot (2 m)}}$

Pull terms out from under the radical.

$\sqrt{9 m^{2} \sqrt[3]{2 m}}$

Rewrite $9 m^{2} \sqrt[3]{2 m}$ as ${(3 m)}^{2} \sqrt[3]{2 m}$ .

Rewrite $9$ as $3^{2}$ .

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

Rewrite $3^{2} m^{2}$ as ${(3 m)}^{2}$ .

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

Pull terms out from under the radical.

$3 m \sqrt{\sqrt[3]{2 m}}$

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

$3 m \sqrt[6]{2 m}$