Find the cube roots of $2744$ by prime factorisation method.

Find the cube roots of $4096$ by prime factorisation method.

Find the cube roots of $8000$ by prime factorisation method.

Find the cube roots of $91125$ by prime factorisation method.

Show that: $\sqrt[3]{125\times 216}=\sqrt[3]{125}\times \sqrt[3]{216}$.

Show that: $\sqrt[3]{343\times 512}=\sqrt[3]{343}\times \sqrt[3]{512}$.

What smallest multiplied to $83349$ So that the product is a perfect cube? Find the cube root of the new number.

Verify that: 

$\sqrt[3 ]{\frac{512 }{1000 }}= \frac{\sqrt[3]{512 }}{\sqrt[3 ]{1000 }}$