Finite Math Examples

$v^{2 \sqrt{96 v x^{2}}} - 9 x \sqrt{54 v^{5}}$

Step 1

Rewrite $96 v x^{2}$ as ${(4 x)}^{2} \cdot (6 v)$ .

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Step 1.1

Factor $16$ out of $96$ .

$v^{2 \sqrt{16 (6) v x^{2}}} - 9 x \sqrt{54 v^{5}}$

Step 1.2

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

$v^{2 \sqrt{4^{2} \cdot 6 v x^{2}}} - 9 x \sqrt{54 v^{5}}$

Step 1.3

Move $v$ .

$v^{2 \sqrt{4^{2} \cdot 6 x^{2} v}} - 9 x \sqrt{54 v^{5}}$

Step 1.4

Move $6$ .

$v^{2 \sqrt{4^{2} x^{2} \cdot 6 v}} - 9 x \sqrt{54 v^{5}}$

Step 1.5

Rewrite $4^{2} x^{2}$ as ${(4 x)}^{2}$ .

$v^{2 \sqrt{{(4 x)}^{2} \cdot 6 v}} - 9 x \sqrt{54 v^{5}}$

Step 1.6

Add parentheses.

$v^{2 \sqrt{{(4 x)}^{2} \cdot (6 v)}} - 9 x \sqrt{54 v^{5}}$

Step 2

Pull terms out from under the radical.

$v^{2 (4 x \sqrt{6 v})} - 9 x \sqrt{54 v^{5}}$

Step 3

Multiply $4$ by $2$ .

$v^{8 (x \sqrt{6 v})} - 9 x \sqrt{54 v^{5}}$

Step 4

Rewrite $54 v^{5}$ as ${(3 v^{2})}^{2} \cdot (6 v)$ .

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Step 4.1

Factor $9$ out of $54$ .

$v^{8 x \sqrt{6 v}} - 9 x \sqrt{9 (6) v^{5}}$

Step 4.2

Rewrite $9$ as $3^{2}$ .

$v^{8 x \sqrt{6 v}} - 9 x \sqrt{3^{2} \cdot 6 v^{5}}$

Step 4.3

Factor out $v^{4}$ .

$v^{8 x \sqrt{6 v}} - 9 x \sqrt{3^{2} \cdot 6 (v^{4} v)}$

Step 4.4

Rewrite $v^{4}$ as ${(v^{2})}^{2}$ .

$v^{8 x \sqrt{6 v}} - 9 x \sqrt{3^{2} \cdot 6 ({(v^{2})}^{2} v)}$

Step 4.5

Move $6$ .

$v^{8 x \sqrt{6 v}} - 9 x \sqrt{3^{2} {(v^{2})}^{2} \cdot 6 v}$

Step 4.6

Rewrite $3^{2} {(v^{2})}^{2}$ as ${(3 v^{2})}^{2}$ .

$v^{8 x \sqrt{6 v}} - 9 x \sqrt{{(3 v^{2})}^{2} \cdot 6 v}$

Step 4.7

Add parentheses.

$v^{8 x \sqrt{6 v}} - 9 x \sqrt{{(3 v^{2})}^{2} \cdot (6 v)}$

Step 5

Pull terms out from under the radical.

$v^{8 x \sqrt{6 v}} - 9 x (3 v^{2} \sqrt{6 v})$

Step 6

Multiply $3$ by $- 9$ .

$v^{8 x \sqrt{6 v}} - 27 x v^{2} \sqrt{6 v}$