Simplify ( cube root of 12j^3)( cube root of 3j^4)

$(\sqrt[3]{12 j^{3}}) (\sqrt[3]{3 j^{4}})$

Step 1

Reorder $12$ and $j^{3}$ .

$\sqrt[3]{j^{3} \cdot 12} \sqrt[3]{3 j^{4}}$

Step 2

Pull terms out from under the radical.

$j \sqrt[3]{12} \sqrt[3]{3 j^{4}}$

Step 3

Rewrite $3 j^{4}$ as $j^{3} \cdot (3 j)$ .

Factor out $j^{3}$ .

$j \sqrt[3]{12} \sqrt[3]{3 (j^{3} j)}$

Reorder $3$ and $j^{3}$ .

$j \sqrt[3]{12} \sqrt[3]{j^{3} \cdot 3 j}$

Add parentheses.

$j \sqrt[3]{12} \sqrt[3]{j^{3} \cdot (3 j)}$

$j \sqrt[3]{12} \sqrt[3]{j^{3} \cdot (3 j)}$

Step 4

Pull terms out from under the radical.

$j \sqrt[3]{12} (j \sqrt[3]{3 j})$

Step 5

Multiply $j$ by $j$ by adding the exponents.

Move $j$ .

$j \cdot j \sqrt[3]{12} \sqrt[3]{3 j}$

Multiply $j$ by $j$ .

$j^{2} \sqrt[3]{12} \sqrt[3]{3 j}$

$j^{2} \sqrt[3]{12} \sqrt[3]{3 j}$

Step 6

Multiply $j^{2} \sqrt[3]{12} \sqrt[3]{3 j}$ .

Combine using the product rule for radicals.

$j^{2} \sqrt[3]{3 j \cdot 12}$

Multiply $12$ by $3$ .

$j^{2} \sqrt[3]{36 j}$

$j^{2} \sqrt[3]{36 j}$

Related Questions