Algebra Examples

$(6 \sqrt[3]{16} - 10 \sqrt[3]{32}) \div 2 \sqrt[3]{2}$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $16$ as $2^{3} \cdot 2$ .

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Step 1.1.1

Factor $8$ out of $16$ .

$(6 \sqrt[3]{8 (2)} - 10 \sqrt[3]{32}) \div 2 \sqrt[3]{2}$

Step 1.1.2

Rewrite $8$ as $2^{3}$ .

$(6 \sqrt[3]{2^{3} \cdot 2} - 10 \sqrt[3]{32}) \div 2 \sqrt[3]{2}$

Step 1.2

Pull terms out from under the radical.

$(6 (2 \sqrt[3]{2}) - 10 \sqrt[3]{32}) \div 2 \sqrt[3]{2}$

Step 1.3

Multiply $2$ by $6$ .

$(12 \sqrt[3]{2} - 10 \sqrt[3]{32}) \div 2 \sqrt[3]{2}$

Step 1.4

Rewrite $32$ as $2^{3} \cdot 4$ .

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Step 1.4.1

Factor $8$ out of $32$ .

$(12 \sqrt[3]{2} - 10 \sqrt[3]{8 (4)}) \div 2 \sqrt[3]{2}$

Step 1.4.2

Rewrite $8$ as $2^{3}$ .

$(12 \sqrt[3]{2} - 10 \sqrt[3]{2^{3} \cdot 4}) \div 2 \sqrt[3]{2}$

Step 1.5

Pull terms out from under the radical.

$(12 \sqrt[3]{2} - 10 (2 \sqrt[3]{4})) \div 2 \sqrt[3]{2}$

Step 1.6

Multiply $2$ by $- 10$ .

$(12 \sqrt[3]{2} - 20 \sqrt[3]{4}) \div 2 \sqrt[3]{2}$

Step 2

Rewrite the division as a fraction.

$\frac{12 \sqrt[3]{2} - 20 \sqrt[3]{4}}{2} \sqrt[3]{2}$

Step 3

Cancel the common factor of $12 \sqrt[3]{2} - 20 \sqrt[3]{4}$ and $2$ .

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Step 3.1

Factor $2$ out of $12 \sqrt[3]{2}$ .

$\frac{2 (6 \sqrt[3]{2}) - 20 \sqrt[3]{4}}{2} \sqrt[3]{2}$

Step 3.2

Factor $2$ out of $- 20 \sqrt[3]{4}$ .

$\frac{2 (6 \sqrt[3]{2}) + 2 (- 10 \sqrt[3]{4})}{2} \sqrt[3]{2}$

Step 3.3

Factor $2$ out of $2 (6 \sqrt[3]{2}) + 2 (- 10 \sqrt[3]{4})$ .

$\frac{2 (6 \sqrt[3]{2} - 10 \sqrt[3]{4})}{2} \sqrt[3]{2}$

Step 3.4

Cancel the common factors.

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Step 3.4.1

Factor $2$ out of $2$ .

$\frac{2 (6 \sqrt[3]{2} - 10 \sqrt[3]{4})}{2 (1)} \sqrt[3]{2}$

Step 3.4.2

Cancel the common factor.

$\frac{2 (6 \sqrt[3]{2} - 10 \sqrt[3]{4})}{2 \cdot 1} \sqrt[3]{2}$

Step 3.4.3

Rewrite the expression.

$\frac{6 \sqrt[3]{2} - 10 \sqrt[3]{4}}{1} \sqrt[3]{2}$

Step 3.4.4

Divide $6 \sqrt[3]{2} - 10 \sqrt[3]{4}$ by $1$ .

$(6 \sqrt[3]{2} - 10 \sqrt[3]{4}) \sqrt[3]{2}$

Step 4

Apply the distributive property.

$6 \sqrt[3]{2} \sqrt[3]{2} - 10 \sqrt[3]{4} \sqrt[3]{2}$

Step 5

Multiply $6 \sqrt[3]{2} \sqrt[3]{2}$ .

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Step 5.1

Raise $\sqrt[3]{2}$ to the power of $1$ .

$6 ({\sqrt[3]{2}}^{1} \sqrt[3]{2}) - 10 \sqrt[3]{4} \sqrt[3]{2}$

Step 5.2

Raise $\sqrt[3]{2}$ to the power of $1$ .

$6 ({\sqrt[3]{2}}^{1} {\sqrt[3]{2}}^{1}) - 10 \sqrt[3]{4} \sqrt[3]{2}$

Step 5.3

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

$6 {\sqrt[3]{2}}^{1 + 1} - 10 \sqrt[3]{4} \sqrt[3]{2}$

Step 5.4

Add $1$ and $1$ .

$6 {\sqrt[3]{2}}^{2} - 10 \sqrt[3]{4} \sqrt[3]{2}$

Step 6

Multiply $- 10 \sqrt[3]{4} \sqrt[3]{2}$ .

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Step 6.1

Combine using the product rule for radicals.

$6 {\sqrt[3]{2}}^{2} - 10 \sqrt[3]{2 \cdot 4}$

Step 6.2

Multiply $2$ by $4$ .

$6 {\sqrt[3]{2}}^{2} - 10 \sqrt[3]{8}$

Step 7

Simplify each term.

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Step 7.1

Rewrite ${\sqrt[3]{2}}^{2}$ as $\sqrt[3]{2^{2}}$ .

$6 \sqrt[3]{2^{2}} - 10 \sqrt[3]{8}$

Step 7.2

Raise $2$ to the power of $2$ .

$6 \sqrt[3]{4} - 10 \sqrt[3]{8}$

Step 7.3

Rewrite $8$ as $2^{3}$ .

$6 \sqrt[3]{4} - 10 \sqrt[3]{2^{3}}$

Step 7.4

Pull terms out from under the radical.

$6 \sqrt[3]{4} - 10 \cdot 2$

Step 7.5

Multiply $- 10$ by $2$ .

$6 \sqrt[3]{4} - 20$

Step 8

The result can be shown in multiple forms.

Exact Form:

$6 \sqrt[3]{4} - 20$

Decimal Form:

$- 10.47559368 \dots$