Algebra Examples

$3 \sqrt[4]{27 x^{3}} \cdot 2 \sqrt[4]{3 x^{5}}$

Step 1

Multiply $2$ by $3$ .

$6 \sqrt[4]{27 x^{3}} \sqrt[4]{3 x^{5}}$

Step 2

Rewrite $3 x^{5}$ as $x^{4} \cdot (3 x)$ .

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Step 2.1

Factor out $x^{4}$ .

$6 \sqrt[4]{27 x^{3}} \sqrt[4]{3 (x^{4} x)}$

Step 2.2

Reorder $3$ and $x^{4}$ .

$6 \sqrt[4]{27 x^{3}} \sqrt[4]{x^{4} \cdot 3 x}$

Step 2.3

Add parentheses.

$6 \sqrt[4]{27 x^{3}} \sqrt[4]{x^{4} \cdot (3 x)}$

Step 3

Pull terms out from under the radical.

$6 \sqrt[4]{27 x^{3}} (| x | \sqrt[4]{3 x})$

Step 4

Multiply $6 \sqrt[4]{27 x^{3}} (| x | \sqrt[4]{3 x})$ .

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Step 4.1

Combine using the product rule for radicals.

$6 \sqrt[4]{3 x (27 x^{3})} | x |$

Step 4.2

Multiply $27$ by $3$ .

$6 \sqrt[4]{81 x \cdot x^{3}} | x |$

Step 4.3

Multiply $x$ by $x^{3}$ by adding the exponents.

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Step 4.3.1

Move $x^{3}$ .

$6 \sqrt[4]{81 (x^{3} x)} | x |$

Step 4.3.2

Multiply $x^{3}$ by $x$ .

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Step 4.3.2.1

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

$6 \sqrt[4]{81 (x^{3} x^{1})} | x |$

Step 4.3.2.2

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

$6 \sqrt[4]{81 x^{3 + 1}} | x |$

Step 4.3.3

Add $3$ and $1$ .

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

Step 5

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

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

Step 6

Pull terms out from under the radical.

$6 | 3 x | | x |$

Step 7

Remove non-negative terms from the absolute value.

$6 (3 | x |) | x |$

Step 8

Multiply $3$ by $6$ .

$18 | x | | x |$

Step 9

Multiply $18 | x | | x |$ .

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Step 9.1

To multiply absolute values, multiply the terms inside each absolute value.

$18 | x \cdot x |$

Step 9.2

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

$18 | x^{1} x |$

Step 9.3

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

$18 | x^{1} x^{1} |$

Step 9.4

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

$18 | x^{1 + 1} |$

Step 9.5

Add $1$ and $1$ .

$18 | x^{2} |$

Step 10

Remove non-negative terms from the absolute value.

$18 x^{2}$