Algebra Examples

$\sqrt[4]{x^{8} z^{16}} \div \sqrt[3]{x^{3} z^{9}}$

Step 1

Rewrite the division as a fraction.

$\frac{\sqrt[4]{x^{8} z^{16}}}{\sqrt[3]{x^{3} z^{9}}}$

Step 2

Simplify the numerator.

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Step 2.1

Rewrite $x^{8} z^{16}$ as ${(x^{2} z^{4})}^{4}$ .

$\frac{\sqrt[4]{{(x^{2} z^{4})}^{4}}}{\sqrt[3]{x^{3} z^{9}}}$

Step 2.2

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

$\frac{x^{2} z^{4}}{\sqrt[3]{x^{3} z^{9}}}$

Step 3

Simplify the denominator.

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Step 3.1

Rewrite $x^{3} z^{9}$ as ${(x z^{3})}^{3}$ .

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

Step 3.2

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

$\frac{x^{2} z^{4}}{x z^{3}}$

Step 4

Reduce the expression by cancelling the common factors.

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Step 4.1

Cancel the common factor of $x^{2}$ and $x$ .

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Step 4.1.1

Factor $x$ out of $x^{2} z^{4}$ .

$\frac{x (x z^{4})}{x z^{3}}$

Step 4.1.2

Cancel the common factors.

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Step 4.1.2.1

Factor $x$ out of $x z^{3}$ .

$\frac{x (x z^{4})}{x (z^{3})}$

Step 4.1.2.2

Cancel the common factor.

$\frac{x (x z^{4})}{x z^{3}}$

Step 4.1.2.3

Rewrite the expression.

$\frac{x z^{4}}{z^{3}}$

Step 4.2

Cancel the common factor of $z^{4}$ and $z^{3}$ .

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Step 4.2.1

Factor $z^{3}$ out of $x z^{4}$ .

$\frac{z^{3} (x z)}{z^{3}}$

Step 4.2.2

Cancel the common factors.

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Step 4.2.2.1

Multiply by $1$ .

$\frac{z^{3} (x z)}{z^{3} \cdot 1}$

Step 4.2.2.2

Cancel the common factor.

$\frac{z^{3} (x z)}{z^{3} \cdot 1}$

Step 4.2.2.3

Rewrite the expression.

$\frac{x z}{1}$

Step 4.2.2.4

Divide $x z$ by $1$ .

$x z$