Algebra Examples

$6 \sqrt[4]{3} \div 2 \sqrt[4]{243}$

Step 1

Rewrite the division as a fraction.

$\frac{6 \sqrt[4]{3}}{2 \sqrt[4]{243}}$

Step 2

Cancel the common factor of $6$ and $2$ .

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Step 2.1

Factor $2$ out of $6 \sqrt[4]{3}$ .

$\frac{2 (3 \sqrt[4]{3})}{2 \sqrt[4]{243}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $2$ out of $2 \sqrt[4]{243}$ .

$\frac{2 (3 \sqrt[4]{3})}{2 (\sqrt[4]{243})}$

Step 2.2.2

Cancel the common factor.

$\frac{2 (3 \sqrt[4]{3})}{2 \sqrt[4]{243}}$

Step 2.2.3

Rewrite the expression.

$\frac{3 \sqrt[4]{3}}{\sqrt[4]{243}}$

Step 3

Combine $\sqrt[4]{3}$ and $\sqrt[4]{243}$ into a single radical.

$3 \sqrt[4]{\frac{3}{243}}$

Step 4

Cancel the common factor of $3$ and $243$ .

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Step 4.1

Factor $3$ out of $3$ .

$3 \sqrt[4]{\frac{3 (1)}{243}}$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $3$ out of $243$ .

$3 \sqrt[4]{\frac{3 \cdot 1}{3 \cdot 81}}$

Step 4.2.2

Cancel the common factor.

$3 \sqrt[4]{\frac{3 \cdot 1}{3 \cdot 81}}$

Step 4.2.3

Rewrite the expression.

$3 \sqrt[4]{\frac{1}{81}}$

Step 5

Rewrite $\sqrt[4]{\frac{1}{81}}$ as $\frac{\sqrt[4]{1}}{\sqrt[4]{81}}$ .

$3 \frac{\sqrt[4]{1}}{\sqrt[4]{81}}$

Step 6

Any root of $1$ is $1$ .

$3 \frac{1}{\sqrt[4]{81}}$

Step 7

Simplify the denominator.

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Step 7.1

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

$3 \frac{1}{\sqrt[4]{3^{4}}}$

Step 7.2

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

$3 (\frac{1}{3})$

Step 8

Cancel the common factor of $3$ .

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Step 8.1

Cancel the common factor.

$3 (\frac{1}{3})$

Step 8.2

Rewrite the expression.

$1$