Algebra Examples

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

Step 1

Rewrite the division as a fraction.

$\frac{6 \sqrt[3]{16} - 10 \sqrt[3]{32}}{2 \sqrt[3]{2}}$

Step 2

Cancel the common factor of $6 \sqrt[3]{16} - 10 \sqrt[3]{32}$ and $2$ .

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Step 2.1

Factor $2$ out of $6 \sqrt[3]{16}$ .

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

Step 2.2

Factor $2$ out of $- 10 \sqrt[3]{32}$ .

$\frac{2 (3 \sqrt[3]{16}) + 2 (- 5 \sqrt[3]{32})}{2 \sqrt[3]{2}}$

Step 2.3

Factor $2$ out of $2 (3 \sqrt[3]{16}) + 2 (- 5 \sqrt[3]{32})$ .

$\frac{2 (3 \sqrt[3]{16} - 5 \sqrt[3]{32})}{2 \sqrt[3]{2}}$

Step 2.4

Cancel the common factors.

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Step 2.4.1

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

$\frac{2 (3 \sqrt[3]{16} - 5 \sqrt[3]{32})}{2 (\sqrt[3]{2})}$

Step 2.4.2

Cancel the common factor.

$\frac{2 (3 \sqrt[3]{16} - 5 \sqrt[3]{32})}{2 \sqrt[3]{2}}$

Step 2.4.3

Rewrite the expression.

$\frac{3 \sqrt[3]{16} - 5 \sqrt[3]{32}}{\sqrt[3]{2}}$

Step 3

Simplify the numerator.

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Step 3.1

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

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Step 3.1.1

Factor $8$ out of $16$ .

$\frac{3 \sqrt[3]{8 (2)} - 5 \sqrt[3]{32}}{\sqrt[3]{2}}$

Step 3.1.2

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

$\frac{3 \sqrt[3]{2^{3} \cdot 2} - 5 \sqrt[3]{32}}{\sqrt[3]{2}}$

Step 3.2

Pull terms out from under the radical.

$\frac{3 (2 \sqrt[3]{2}) - 5 \sqrt[3]{32}}{\sqrt[3]{2}}$

Step 3.3

Multiply $2$ by $3$ .

$\frac{6 \sqrt[3]{2} - 5 \sqrt[3]{32}}{\sqrt[3]{2}}$

Step 3.4

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

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Step 3.4.1

Factor $8$ out of $32$ .

$\frac{6 \sqrt[3]{2} - 5 \sqrt[3]{8 (4)}}{\sqrt[3]{2}}$

Step 3.4.2

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

$\frac{6 \sqrt[3]{2} - 5 \sqrt[3]{2^{3} \cdot 4}}{\sqrt[3]{2}}$

Step 3.5

Pull terms out from under the radical.

$\frac{6 \sqrt[3]{2} - 5 (2 \sqrt[3]{4})}{\sqrt[3]{2}}$

Step 3.6

Multiply $2$ by $- 5$ .

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

Step 4

Multiply $\frac{6 \sqrt[3]{2} - 10 \sqrt[3]{4}}{\sqrt[3]{2}}$ by $\frac{{\sqrt[3]{2}}^{2}}{{\sqrt[3]{2}}^{2}}$ .

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

Step 5

Combine and simplify the denominator.

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Step 5.1

Multiply $\frac{6 \sqrt[3]{2} - 10 \sqrt[3]{4}}{\sqrt[3]{2}}$ by $\frac{{\sqrt[3]{2}}^{2}}{{\sqrt[3]{2}}^{2}}$ .

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

Step 5.2

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

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

Step 5.3

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

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

Step 5.4

Add $1$ and $2$ .

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

Step 5.5

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

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Step 5.5.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{2}$ as $2^{\frac{1}{3}}$ .

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

Step 5.5.2

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

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

Step 5.5.3

Combine $\frac{1}{3}$ and $3$ .

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

Step 5.5.4

Cancel the common factor of $3$ .

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Step 5.5.4.1

Cancel the common factor.

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

Step 5.5.4.2

Rewrite the expression.

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

Step 5.5.5

Evaluate the exponent.

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

Step 6

Cancel the common factor of $6 \sqrt[3]{2} - 10 \sqrt[3]{4}$ and $2$ .

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Step 6.1

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

$\frac{2 ((3 \sqrt[3]{2} - 5 \sqrt[3]{4}) {\sqrt[3]{2}}^{2})}{2}$

Step 6.2

Cancel the common factors.

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Step 6.2.1

Factor $2$ out of $2$ .

$\frac{2 ((3 \sqrt[3]{2} - 5 \sqrt[3]{4}) {\sqrt[3]{2}}^{2})}{2 (1)}$

Step 6.2.2

Cancel the common factor.

$\frac{2 ((3 \sqrt[3]{2} - 5 \sqrt[3]{4}) {\sqrt[3]{2}}^{2})}{2 \cdot 1}$

Step 6.2.3

Rewrite the expression.

$\frac{(3 \sqrt[3]{2} - 5 \sqrt[3]{4}) {\sqrt[3]{2}}^{2}}{1}$

Step 6.2.4

Divide $(3 \sqrt[3]{2} - 5 \sqrt[3]{4}) {\sqrt[3]{2}}^{2}$ by $1$ .

$(3 \sqrt[3]{2} - 5 \sqrt[3]{4}) {\sqrt[3]{2}}^{2}$

Step 7

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

$(3 \sqrt[3]{2} - 5 \sqrt[3]{4}) \sqrt[3]{2^{2}}$

Step 8

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

$(3 \sqrt[3]{2} - 5 \sqrt[3]{4}) \sqrt[3]{4}$

Step 9

Apply the distributive property.

$3 \sqrt[3]{2} \sqrt[3]{4} - 5 \sqrt[3]{4} \sqrt[3]{4}$

Step 10

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

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Step 10.1

Combine using the product rule for radicals.

$3 \sqrt[3]{4 \cdot 2} - 5 \sqrt[3]{4} \sqrt[3]{4}$

Step 10.2

Multiply $4$ by $2$ .

$3 \sqrt[3]{8} - 5 \sqrt[3]{4} \sqrt[3]{4}$

Step 11

Multiply $- 5 \sqrt[3]{4} \sqrt[3]{4}$ .

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Step 11.1

Raise $\sqrt[3]{4}$ to the power of $1$ .

$3 \sqrt[3]{8} - 5 ({\sqrt[3]{4}}^{1} \sqrt[3]{4})$

Step 11.2

Raise $\sqrt[3]{4}$ to the power of $1$ .

$3 \sqrt[3]{8} - 5 ({\sqrt[3]{4}}^{1} {\sqrt[3]{4}}^{1})$

Step 11.3

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

$3 \sqrt[3]{8} - 5 {\sqrt[3]{4}}^{1 + 1}$

Step 11.4

Add $1$ and $1$ .

$3 \sqrt[3]{8} - 5 {\sqrt[3]{4}}^{2}$

Step 12

Simplify each term.

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Step 12.1

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

$3 \sqrt[3]{2^{3}} - 5 {\sqrt[3]{4}}^{2}$

Step 12.2

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

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

Step 12.3

Multiply $3$ by $2$ .

$6 - 5 {\sqrt[3]{4}}^{2}$

Step 12.4

Rewrite ${\sqrt[3]{4}}^{2}$ as $\sqrt[3]{4^{2}}$ .

$6 - 5 \sqrt[3]{4^{2}}$

Step 12.5

Raise $4$ to the power of $2$ .

$6 - 5 \sqrt[3]{16}$

Step 12.6

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

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Step 12.6.1

Factor $8$ out of $16$ .

$6 - 5 \sqrt[3]{8 (2)}$

Step 12.6.2

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

$6 - 5 \sqrt[3]{2^{3} \cdot 2}$

Step 12.7

Pull terms out from under the radical.

$6 - 5 (2 \sqrt[3]{2})$

Step 12.8

Multiply $2$ by $- 5$ .

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

Step 13

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$- 6.59921049 \dots$