Algebra Examples

$18 x^{2} \sqrt{14 x^{8}} \div 6 \sqrt{7 x^{4}}$

Step 1

Rewrite the division as a fraction.

$\frac{18 x^{2} \sqrt{14 x^{8}}}{6 \sqrt{7 x^{4}}}$

Step 2

Cancel the common factor of $18$ and $6$ .

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Step 2.1

Factor $6$ out of $18 x^{2} \sqrt{14 x^{8}}$ .

$\frac{6 (3 x^{2} \sqrt{14 x^{8}})}{6 \sqrt{7 x^{4}}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $6$ out of $6 \sqrt{7 x^{4}}$ .

$\frac{6 (3 x^{2} \sqrt{14 x^{8}})}{6 (\sqrt{7 x^{4}})}$

Step 2.2.2

Cancel the common factor.

$\frac{6 (3 x^{2} \sqrt{14 x^{8}})}{6 \sqrt{7 x^{4}}}$

Step 2.2.3

Rewrite the expression.

$\frac{3 x^{2} \sqrt{14 x^{8}}}{\sqrt{7 x^{4}}}$

Step 3

Combine $\sqrt{14 x^{8}}$ and $\sqrt{7 x^{4}}$ into a single radical.

$3 x^{2} \sqrt{\frac{14 x^{8}}{7 x^{4}}}$

Step 4

Reduce the expression $\frac{14 x^{8}}{7 x^{4}}$ by cancelling the common factors.

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Step 4.1

Factor $7$ out of $14 x^{8}$ .

$3 x^{2} \sqrt{\frac{7 (2 x^{8})}{7 x^{4}}}$

Step 4.2

Factor $7$ out of $7 x^{4}$ .

$3 x^{2} \sqrt{\frac{7 (2 x^{8})}{7 (x^{4})}}$

Step 4.3

Cancel the common factor.

$3 x^{2} \sqrt{\frac{7 (2 x^{8})}{7 x^{4}}}$

Step 4.4

Rewrite the expression.

$3 x^{2} \sqrt{\frac{2 x^{8}}{x^{4}}}$

Step 5

Cancel the common factor of $x^{8}$ and $x^{4}$ .

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Step 5.1

Factor $x^{4}$ out of $2 x^{8}$ .

$3 x^{2} \sqrt{\frac{x^{4} (2 x^{4})}{x^{4}}}$

Step 5.2

Cancel the common factors.

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Step 5.2.1

Multiply by $1$ .

$3 x^{2} \sqrt{\frac{x^{4} (2 x^{4})}{x^{4} \cdot 1}}$

Step 5.2.2

Cancel the common factor.

$3 x^{2} \sqrt{\frac{x^{4} (2 x^{4})}{x^{4} \cdot 1}}$

Step 5.2.3

Rewrite the expression.

$3 x^{2} \sqrt{\frac{2 x^{4}}{1}}$

Step 5.2.4

Divide $2 x^{4}$ by $1$ .

$3 x^{2} \sqrt{2 x^{4}}$

Step 6

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

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Step 6.1

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

$3 x^{2} \sqrt{2 {(x^{2})}^{2}}$

Step 6.2

Reorder $2$ and ${(x^{2})}^{2}$ .

$3 x^{2} \sqrt{{(x^{2})}^{2} \cdot 2}$

Step 7

Pull terms out from under the radical.

$3 x^{2} (x^{2} \sqrt{2})$

Step 8

Multiply $x^{2}$ by $x^{2}$ by adding the exponents.

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Step 8.1

Move $x^{2}$ .

$3 (x^{2} x^{2}) \sqrt{2}$

Step 8.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$3 x^{2 + 2} \sqrt{2}$

Step 8.3

Add $2$ and $2$ .

$3 x^{4} \sqrt{2}$