Simplify ( square root of (4x^2)/(2^4))( square root of (9x^4)/(3^6))

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

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

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

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

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

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

Cancel the common factors.

Factor $4$ out of $16$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

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

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

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

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

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

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

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

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

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

Cancel the common factors.

Factor $9$ out of $729$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Simplify the expression.

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

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

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

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

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

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

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

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

Combine.

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

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

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

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

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

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

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

Add $1$ and $2$ .

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

Multiply $2$ by $9$ .

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

Simplify ( square root of (4x^2)/(2^4))( square root of (9x^4)/(3^6))

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