Pre-Algebra Examples

${(\sqrt[12]{2 y})}^{8}$

Step 1

Rewrite ${\sqrt[12]{2 y}}^{8}$ as $\sqrt[12]{{(2 y)}^{8}}$ .

$\sqrt[12]{{(2 y)}^{8}}$

Step 2

Apply the product rule to $2 y$ .

$\sqrt[12]{2^{8} y^{8}}$

Step 3

Raise $2$ to the power of $8$ .

$\sqrt[12]{256 y^{8}}$

Step 4

Rewrite $256 y^{8}$ as ${(4 y^{2})}^{4}$ .

$\sqrt[12]{{(4 y^{2})}^{4}}$

Step 5

Rewrite $\sqrt[12]{{(4 y^{2})}^{4}}$ as $\sqrt[3]{\sqrt[4]{{(4 y^{2})}^{4}}}$ .

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

Step 6

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

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