Algebra Examples

$(\sqrt{\frac{4 x^{2}}{2^{4}}}) (\sqrt{\frac{9 x^{4}}{3^{6}}})$

Step 1

Raise $2$ to the power of $4$ .

$\sqrt{\frac{4 x^{2}}{16}} \sqrt{\frac{9 x^{4}}{3^{6}}}$

Step 2

Cancel the common factor of $4$ and $16$ .

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Step 2.1

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

$\sqrt{\frac{4 (x^{2})}{16}} \sqrt{\frac{9 x^{4}}{3^{6}}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $4$ out of $16$ .

$\sqrt{\frac{4 x^{2}}{4 \cdot 4}} \sqrt{\frac{9 x^{4}}{3^{6}}}$

Step 2.2.2

Cancel the common factor.

$\sqrt{\frac{4 x^{2}}{4 \cdot 4}} \sqrt{\frac{9 x^{4}}{3^{6}}}$

Step 2.2.3

Rewrite the expression.

$\sqrt{\frac{x^{2}}{4}} \sqrt{\frac{9 x^{4}}{3^{6}}}$

Step 3

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

$\sqrt{\frac{x^{2}}{2^{2}}} \sqrt{\frac{9 x^{4}}{3^{6}}}$

Step 4

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

$\sqrt{{(\frac{x}{2})}^{2}} \sqrt{\frac{9 x^{4}}{3^{6}}}$

Step 5

Pull terms out from under the radical, assuming positive real numbers.

$\frac{x}{2} \sqrt{\frac{9 x^{4}}{3^{6}}}$

Step 6

Raise $3$ to the power of $6$ .

$\frac{x}{2} \sqrt{\frac{9 x^{4}}{729}}$

Step 7

Cancel the common factor of $9$ and $729$ .

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Step 7.1

Factor $9$ out of $9 x^{4}$ .

$\frac{x}{2} \sqrt{\frac{9 (x^{4})}{729}}$

Step 7.2

Cancel the common factors.

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Step 7.2.1

Factor $9$ out of $729$ .

$\frac{x}{2} \sqrt{\frac{9 x^{4}}{9 \cdot 81}}$

Step 7.2.2

Cancel the common factor.

$\frac{x}{2} \sqrt{\frac{9 x^{4}}{9 \cdot 81}}$

Step 7.2.3

Rewrite the expression.

$\frac{x}{2} \sqrt{\frac{x^{4}}{81}}$

Step 8

Simplify the expression.

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Step 8.1

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

$\frac{x}{2} \sqrt{\frac{{(x^{2})}^{2}}{81}}$

Step 8.2

Rewrite $81$ as $9^{2}$ .

$\frac{x}{2} \sqrt{\frac{{(x^{2})}^{2}}{9^{2}}}$

Step 9

Rewrite $\frac{{(x^{2})}^{2}}{9^{2}}$ as ${(\frac{x^{2}}{9})}^{2}$ .

$\frac{x}{2} \sqrt{{(\frac{x^{2}}{9})}^{2}}$

Step 10

Pull terms out from under the radical, assuming positive real numbers.

$\frac{x}{2} \cdot \frac{x^{2}}{9}$

Step 11

Combine.

$\frac{x \cdot x^{2}}{2 \cdot 9}$

Step 12

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

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Step 12.1

Multiply $x$ by $x^{2}$ .

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Step 12.1.1

Raise $x$ to the power of $1$ .

$\frac{x^{1} x^{2}}{2 \cdot 9}$

Step 12.1.2

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

$\frac{x^{1 + 2}}{2 \cdot 9}$

Step 12.2

Add $1$ and $2$ .

$\frac{x^{3}}{2 \cdot 9}$

Step 13

Multiply $2$ by $9$ .

$\frac{x^{3}}{18}$