Simplify (28 cube root of -16m^6)/(4 cube root of 2m)

$\frac{28 \sqrt[3]{- 16 m^{6}}}{4 \sqrt[3]{2 m}}$

Step 1

Cancel the common factor of $28$ and $4$ .

Factor $4$ out of $28 \sqrt[3]{- 16 m^{6}}$ .

$\frac{4 (7 \sqrt[3]{- 16 m^{6}})}{4 \sqrt[3]{2 m}}$

Cancel the common factors.

Factor $4$ out of $4 \sqrt[3]{2 m}$ .

$\frac{4 (7 \sqrt[3]{- 16 m^{6}})}{4 (\sqrt[3]{2 m})}$

Cancel the common factor.

$\frac{4 (7 \sqrt[3]{- 16 m^{6}})}{4 \sqrt[3]{2 m}}$

Rewrite the expression.

$\frac{7 \sqrt[3]{- 16 m^{6}}}{\sqrt[3]{2 m}}$

Step 2

Combine $\sqrt[3]{- 16 m^{6}}$ and $\sqrt[3]{2 m}$ into a single radical.

$7 \sqrt[3]{\frac{- 16 m^{6}}{2 m}}$

Step 3

Reduce the expression $\frac{- 16 m^{6}}{2 m}$ by cancelling the common factors.

Factor $2$ out of $- 16 m^{6}$ .

$7 \sqrt[3]{\frac{2 (- 8 m^{6})}{2 m}}$

Factor $2$ out of $2 m$ .

$7 \sqrt[3]{\frac{2 (- 8 m^{6})}{2 (m)}}$

Cancel the common factor.

$7 \sqrt[3]{\frac{2 (- 8 m^{6})}{2 m}}$

Rewrite the expression.

$7 \sqrt[3]{\frac{- 8 m^{6}}{m}}$

Step 4

Cancel the common factor of $m^{6}$ and $m$ .

Factor $m$ out of $- 8 m^{6}$ .

$7 \sqrt[3]{\frac{m (- 8 m^{5})}{m}}$

Cancel the common factors.

Raise $m$ to the power of $1$ .

$7 \sqrt[3]{\frac{m (- 8 m^{5})}{m^{1}}}$

Factor $m$ out of $m^{1}$ .

$7 \sqrt[3]{\frac{m (- 8 m^{5})}{m \cdot 1}}$

Cancel the common factor.

$7 \sqrt[3]{\frac{m (- 8 m^{5})}{m \cdot 1}}$

Rewrite the expression.

$7 \sqrt[3]{\frac{- 8 m^{5}}{1}}$

Divide $- 8 m^{5}$ by $1$ .

$7 \sqrt[3]{- 8 m^{5}}$

Step 5

Rewrite $- 8 m^{5}$ as ${(- 2 m)}^{3} m^{2}$ .

Rewrite $- 8$ as ${(- 2)}^{3}$ .

$7 \sqrt[3]{{(- 2)}^{3} m^{5}}$

Factor out $m^{3}$ .

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

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

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

Step 6

Pull terms out from under the radical.

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

Step 7

Multiply $- 2$ by $7$ .

$- 14 m \sqrt[3]{m^{2}}$

Simplify (28 cube root of -16m^6)/(4 cube root of 2m)

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