Basic Math Examples

$- 4 \sqrt[4]{8 v^{4}} \cdot \sqrt[4]{40 v^{3}}$

Step 1

Reorder $8$ and $v^{4}$ .

$- 4 \sqrt[4]{v^{4} \cdot 8} \cdot \sqrt[4]{40 v^{3}}$

Step 2

Pull terms out from under the radical.

$- 4 (v \sqrt[4]{8}) \cdot \sqrt[4]{40 v^{3}}$

Step 3

Multiply $- 4 v \sqrt[4]{8} \sqrt[4]{40 v^{3}}$ .

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Step 3.1

Combine using the product rule for radicals.

$- 4 v \sqrt[4]{40 v^{3} \cdot 8}$

Step 3.2

Multiply $8$ by $40$ .

$- 4 v \sqrt[4]{320 v^{3}}$

$- 4 v \sqrt[4]{320 v^{3}}$

Step 4

Rewrite $320 v^{3}$ as $2^{4} \cdot (20 v^{3})$ .

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Step 4.1

Factor $16$ out of $320$ .

$- 4 v \sqrt[4]{16 (20) v^{3}}$

Step 4.2

Rewrite $16$ as $2^{4}$ .

$- 4 v \sqrt[4]{2^{4} \cdot 20 v^{3}}$

Step 4.3

Add parentheses.

$- 4 v \sqrt[4]{2^{4} \cdot (20 v^{3})}$

$- 4 v \sqrt[4]{2^{4} \cdot (20 v^{3})}$

Step 5

Pull terms out from under the radical.

$- 4 v (2 \sqrt[4]{20 v^{3}})$

Step 6

Multiply $2$ by $- 4$ .

$- 8 v \sqrt[4]{20 v^{3}}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$