Simplify fourth root of 16x^2* square root of 121x^3

$\sqrt[4]{16 x^{2}} \cdot \sqrt{121 x^{3}}$

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

$\sqrt[4]{2^{4} x^{2}} \cdot \sqrt{121 x^{3}}$

Pull terms out from under the radical.

$2 \sqrt[4]{x^{2}} \cdot \sqrt{121 x^{3}}$

Rewrite $\sqrt[4]{x^{2}}$ as $\sqrt{\sqrt{x^{2}}}$ .

$2 \sqrt{\sqrt{x^{2}}} \cdot \sqrt{121 x^{3}}$

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

$2 \sqrt{x} \cdot \sqrt{121 x^{3}}$

Rewrite $121 x^{3}$ as ${(11 x)}^{2} x$ .

Rewrite $121$ as $11^{2}$ .

$2 \sqrt{x} \cdot \sqrt{11^{2} x^{3}}$

Factor out $x^{2}$ .

$2 \sqrt{x} \cdot \sqrt{11^{2} (x^{2} x)}$

Rewrite $11^{2} x^{2}$ as ${(11 x)}^{2}$ .

$2 \sqrt{x} \cdot \sqrt{{(11 x)}^{2} x}$

Pull terms out from under the radical.

$2 \sqrt{x} \cdot (11 x \sqrt{x})$

Multiply $2 \sqrt{x} (11 x \sqrt{x})$ .

Multiply $11$ by $2$ .

$22 \sqrt{x} (x \sqrt{x})$

Raise $\sqrt{x}$ to the power of $1$ .

$22 (x ({\sqrt{x}}^{1} \sqrt{x}))$

Raise $\sqrt{x}$ to the power of $1$ .

$22 (x ({\sqrt{x}}^{1} {\sqrt{x}}^{1}))$

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

$22 (x {\sqrt{x}}^{1 + 1})$

Add $1$ and $1$ .

$22 (x {\sqrt{x}}^{2})$

Rewrite ${\sqrt{x}}^{2}$ as $x$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x}$ as $x^{\frac{1}{2}}$ .

$22 (x {(x^{\frac{1}{2}})}^{2})$

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$22 (x \cdot x^{\frac{1}{2} \cdot 2})$

Combine $\frac{1}{2}$ and $2$ .

$22 (x \cdot x^{\frac{2}{2}})$

Cancel the common factor of $2$ .

Cancel the common factor.

$22 (x \cdot x^{\frac{2}{2}})$

Rewrite the expression.

$22 (x \cdot x^{1})$

Simplify.

$22 (x \cdot x)$

Multiply $x$ by $x$ .

$22 x^{2}$