Simplify the Radical Expression -3 cube root of 162k^4+7k cube root of 48k

$- 3 \sqrt[3]{162 k^{4}} + 7 k \sqrt[3]{48 k}$

Step 1

Simplify each term.

Rewrite $162 k^{4}$ as ${(3 k)}^{3} \cdot (6 k)$ .

Factor $27$ out of $162$ .

$- 3 \sqrt[3]{27 (6) k^{4}} + 7 k \sqrt[3]{48 k}$

Rewrite $27$ as $3^{3}$ .

$- 3 \sqrt[3]{3^{3} \cdot 6 k^{4}} + 7 k \sqrt[3]{48 k}$

Factor out $k^{3}$ .

$- 3 \sqrt[3]{3^{3} \cdot 6 (k^{3} k)} + 7 k \sqrt[3]{48 k}$

Move $6$ .

$- 3 \sqrt[3]{3^{3} k^{3} \cdot 6 k} + 7 k \sqrt[3]{48 k}$

Rewrite $3^{3} k^{3}$ as ${(3 k)}^{3}$ .

$- 3 \sqrt[3]{{(3 k)}^{3} \cdot 6 k} + 7 k \sqrt[3]{48 k}$

Add parentheses.

$- 3 \sqrt[3]{{(3 k)}^{3} \cdot (6 k)} + 7 k \sqrt[3]{48 k}$

Pull terms out from under the radical.

$- 3 (3 k \sqrt[3]{6 k}) + 7 k \sqrt[3]{48 k}$

Multiply $3$ by $- 3$ .

$- 9 (k \sqrt[3]{6 k}) + 7 k \sqrt[3]{48 k}$

Rewrite $48 k$ as $2^{3} \cdot (6 k)$ .

Factor $8$ out of $48$ .

$- 9 k \sqrt[3]{6 k} + 7 k \sqrt[3]{8 (6) k}$

Rewrite $8$ as $2^{3}$ .

$- 9 k \sqrt[3]{6 k} + 7 k \sqrt[3]{2^{3} \cdot 6 k}$

Add parentheses.

$- 9 k \sqrt[3]{6 k} + 7 k \sqrt[3]{2^{3} \cdot (6 k)}$

Pull terms out from under the radical.

$- 9 k \sqrt[3]{6 k} + 7 k (2 \sqrt[3]{6 k})$

Multiply $2$ by $7$ .

$- 9 k \sqrt[3]{6 k} + 14 k \sqrt[3]{6 k}$

Step 2

Add $- 9 k \sqrt[3]{6 k}$ and $14 k \sqrt[3]{6 k}$ .

$5 k \sqrt[3]{6 k}$