Basic Math Examples

$- \frac{\sqrt[3]{2 z^{4}}}{8} + \sqrt[3]{\frac{128 z^{4}}{64}}$

Step 1

Simplify each term.

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Step 1.1

Simplify the numerator.

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Step 1.1.1

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

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Step 1.1.1.1

Factor out $z^{3}$ .

$- \frac{\sqrt[3]{2 (z^{3} z)}}{8} + \sqrt[3]{\frac{128 z^{4}}{64}}$

Step 1.1.1.2

Reorder $2$ and $z^{3}$ .

$- \frac{\sqrt[3]{z^{3} \cdot 2 z}}{8} + \sqrt[3]{\frac{128 z^{4}}{64}}$

Step 1.1.1.3

Add parentheses.

$- \frac{\sqrt[3]{z^{3} \cdot (2 z)}}{8} + \sqrt[3]{\frac{128 z^{4}}{64}}$

Step 1.1.2

Pull terms out from under the radical.

$- \frac{z \sqrt[3]{2 z}}{8} + \sqrt[3]{\frac{128 z^{4}}{64}}$

Step 1.2

Reduce the expression by cancelling the common factors.

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Step 1.2.1

Reduce the expression $\frac{128 z^{4}}{64}$ by cancelling the common factors.

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Step 1.2.1.1

Factor $64$ out of $128 z^{4}$ .

$- \frac{z \sqrt[3]{2 z}}{8} + \sqrt[3]{\frac{64 (2 z^{4})}{64}}$

Step 1.2.1.2

Factor $64$ out of $64$ .

$- \frac{z \sqrt[3]{2 z}}{8} + \sqrt[3]{\frac{64 (2 z^{4})}{64 (1)}}$

Step 1.2.1.3

Cancel the common factor.

$- \frac{z \sqrt[3]{2 z}}{8} + \sqrt[3]{\frac{64 (2 z^{4})}{64 \cdot 1}}$

Step 1.2.1.4

Rewrite the expression.

$- \frac{z \sqrt[3]{2 z}}{8} + \sqrt[3]{\frac{2 z^{4}}{1}}$

Step 1.2.2

Divide $2 z^{4}$ by $1$ .

$- \frac{z \sqrt[3]{2 z}}{8} + \sqrt[3]{2 z^{4}}$

Step 1.3

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

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Step 1.3.1

Factor out $z^{3}$ .

$- \frac{z \sqrt[3]{2 z}}{8} + \sqrt[3]{2 (z^{3} z)}$

Step 1.3.2

Reorder $2$ and $z^{3}$ .

$- \frac{z \sqrt[3]{2 z}}{8} + \sqrt[3]{z^{3} \cdot 2 z}$

Step 1.3.3

Add parentheses.

$- \frac{z \sqrt[3]{2 z}}{8} + \sqrt[3]{z^{3} \cdot (2 z)}$

Step 1.4

Pull terms out from under the radical.

$- \frac{z \sqrt[3]{2 z}}{8} + z \sqrt[3]{2 z}$

Step 2

To write $z \sqrt[3]{2 z}$ as a fraction with a common denominator, multiply by $\frac{8}{8}$ .

$- \frac{z \sqrt[3]{2 z}}{8} + z \sqrt[3]{2 z} \cdot \frac{8}{8}$

Step 3

Simplify terms.

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Step 3.1

Combine $z \sqrt[3]{2 z}$ and $\frac{8}{8}$ .

$- \frac{z \sqrt[3]{2 z}}{8} + \frac{z \sqrt[3]{2 z} \cdot 8}{8}$

Step 3.2

Combine the numerators over the common denominator.

$\frac{- z \sqrt[3]{2 z} + z \sqrt[3]{2 z} \cdot 8}{8}$

Step 4

Simplify the numerator.

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Step 4.1

Move $8$ to the left of $z \sqrt[3]{2 z}$ .

$\frac{- z \sqrt[3]{2 z} + 8 \cdot (z \sqrt[3]{2 z})}{8}$

Step 4.2

Add $- z \sqrt[3]{2 z}$ and $8 z \sqrt[3]{2 z}$ .

$\frac{7 z \sqrt[3]{2 z}}{8}$