Simplify square root of 36x* fourth root of 81x^10

$\sqrt{36 x} \cdot \sqrt[4]{81 x^{10}}$

Step 1

Rewrite $36$ as $6^{2}$ .

$\sqrt{6^{2} x} \cdot \sqrt[4]{81 x^{10}}$

Step 2

Pull terms out from under the radical.

$6 \sqrt{x} \cdot \sqrt[4]{81 x^{10}}$

Step 3

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

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

$6 \sqrt{x} \cdot \sqrt[4]{3^{4} x^{10}}$

Factor out $x^{8}$ .

$6 \sqrt{x} \cdot \sqrt[4]{3^{4} (x^{8} x^{2})}$

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

$6 \sqrt{x} \cdot \sqrt[4]{3^{4} ({(x^{2})}^{4} x^{2})}$

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

$6 \sqrt{x} \cdot \sqrt[4]{{(3 x^{2})}^{4} x^{2}}$

Step 4

Pull terms out from under the radical.

$6 \sqrt{x} \cdot (3 x^{2} \sqrt[4]{x^{2}})$

Step 5

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

$6 \sqrt{x} \cdot (3 x^{2} \sqrt{\sqrt{x^{2}}})$

Step 6

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

$6 \sqrt{x} \cdot (3 x^{2} \sqrt{x})$

Step 7

Multiply $6 \sqrt{x} (3 x^{2} \sqrt{x})$ .

Multiply $3$ by $6$ .

$18 \sqrt{x} (x^{2} \sqrt{x})$

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

$18 (x^{2} ({\sqrt{x}}^{1} \sqrt{x}))$

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

$18 (x^{2} ({\sqrt{x}}^{1} {\sqrt{x}}^{1}))$

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

$18 (x^{2} {\sqrt{x}}^{1 + 1})$

Add $1$ and $1$ .

$18 (x^{2} {\sqrt{x}}^{2})$

Step 8

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

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

$18 (x^{2} {(x^{\frac{1}{2}})}^{2})$

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

$18 (x^{2} x^{\frac{1}{2} \cdot 2})$

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

$18 (x^{2} x^{\frac{2}{2}})$

Cancel the common factor of $2$ .

Cancel the common factor.

$18 (x^{2} x^{\frac{2}{2}})$

Rewrite the expression.

$18 (x^{2} x^{1})$

Simplify.

$18 (x^{2} x)$

Step 9

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

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

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

$18 (x^{2} x^{1})$

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

$18 x^{2 + 1}$

Add $2$ and $1$ .

$18 x^{3}$

Simplify square root of 36x* fourth root of 81x^10

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