Simplify fourth root of 81x^10* square root of 121x

$\sqrt[4]{81 x^{10}} \cdot \sqrt{121 x}$

Step 1

Rewrite $81 x^{10}$ as ${(3 x^{2})}^{4} x^{2}$ .

Rewrite $81$ as $3^{4}$ .

$\sqrt[4]{3^{4} x^{10}} \cdot \sqrt{121 x}$

Factor out $x^{8}$ .

$\sqrt[4]{3^{4} (x^{8} x^{2})} \cdot \sqrt{121 x}$

Rewrite $x^{8}$ as ${(x^{2})}^{4}$ .

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

Rewrite $3^{4} {(x^{2})}^{4}$ as ${(3 x^{2})}^{4}$ .

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

Step 2

Pull terms out from under the radical.

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

Step 3

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

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

Step 4

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

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

Step 5

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

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

Step 6

Pull terms out from under the radical.

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

Step 7

Multiply $3 x^{2} \sqrt{x} (11 \sqrt{x})$ .

Multiply $11$ by $3$ .

$33 x^{2} \sqrt{x} \sqrt{x}$

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

$33 x^{2} ({\sqrt{x}}^{1} \sqrt{x})$

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

$33 x^{2} ({\sqrt{x}}^{1} {\sqrt{x}}^{1})$

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

$33 x^{2} {\sqrt{x}}^{1 + 1}$

Add $1$ and $1$ .

$33 x^{2} {\sqrt{x}}^{2}$

Step 8

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

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

$33 x^{2} {(x^{\frac{1}{2}})}^{2}$

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

$33 x^{2} x^{\frac{1}{2} \cdot 2}$

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

$33 x^{2} x^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$33 x^{2} x^{\frac{2}{2}}$

Rewrite the expression.

$33 x^{2} x^{1}$

Simplify.

$33 x^{2} x$

Step 9

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

Move $x$ .

$33 (x \cdot x^{2})$

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

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

$33 (x^{1} x^{2})$

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

$33 x^{1 + 2}$

Add $1$ and $2$ .

$33 x^{3}$

Simplify fourth root of 81x^10* square root of 121x

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