Algebra Examples

${(\sqrt[3]{x^{2} y^{3} z^{4}})}^{2}$

Step 1

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

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Step 1.1

Factor out $z^{3}$ .

${\sqrt[3]{x^{2} y^{3} (z^{3} z)}}^{2}$

Step 1.2

Move $x^{2}$ .

${\sqrt[3]{y^{3} z^{3} x^{2} z}}^{2}$

Step 1.3

Rewrite $y^{3} z^{3}$ as ${(y z)}^{3}$ .

${\sqrt[3]{{(y z)}^{3} x^{2} z}}^{2}$

Step 1.4

Add parentheses.

${\sqrt[3]{{(y z)}^{3} (x^{2} z)}}^{2}$

Step 2

Pull terms out from under the radical.

${(y z \sqrt[3]{x^{2} z})}^{2}$

Step 3

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 3.1

Apply the product rule to $y z \sqrt[3]{x^{2} z}$ .

${(y z)}^{2} {\sqrt[3]{x^{2} z}}^{2}$

Step 3.2

Apply the product rule to $y z$ .

$y^{2} z^{2} {\sqrt[3]{x^{2} z}}^{2}$

Step 4

Rewrite ${\sqrt[3]{x^{2} z}}^{2}$ as $\sqrt[3]{{(x^{2} z)}^{2}}$ .

$y^{2} z^{2} \sqrt[3]{{(x^{2} z)}^{2}}$

Step 5

Apply the product rule to $x^{2} z$ .

$y^{2} z^{2} \sqrt[3]{{(x^{2})}^{2} z^{2}}$

Step 6

Multiply the exponents in ${(x^{2})}^{2}$ .

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Step 6.1

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

$y^{2} z^{2} \sqrt[3]{x^{2 \cdot 2} z^{2}}$

Step 6.2

Multiply $2$ by $2$ .

$y^{2} z^{2} \sqrt[3]{x^{4} z^{2}}$

Step 7

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

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Step 7.1

Factor out $x^{3}$ .

$y^{2} z^{2} \sqrt[3]{x^{3} x z^{2}}$

Step 7.2

Add parentheses.

$y^{2} z^{2} \sqrt[3]{x^{3} (x z^{2})}$

Step 8

Pull terms out from under the radical.

$y^{2} z^{2} x \sqrt[3]{x z^{2}}$