Finite Math Examples

$\sqrt[3]{3} (8 \sqrt[3]{3} - \sqrt[3]{9})$

Step 1

Apply the distributive property.

$\sqrt[3]{3} (8 \sqrt[3]{3}) + \sqrt[3]{3} (- \sqrt[3]{9})$

Step 2

Multiply $\sqrt[3]{3} (8 \sqrt[3]{3})$ .

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Step 2.1

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

$8 ({\sqrt[3]{3}}^{1} \sqrt[3]{3}) + \sqrt[3]{3} (- \sqrt[3]{9})$

Step 2.2

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

$8 ({\sqrt[3]{3}}^{1} {\sqrt[3]{3}}^{1}) + \sqrt[3]{3} (- \sqrt[3]{9})$

Step 2.3

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

$8 {\sqrt[3]{3}}^{1 + 1} + \sqrt[3]{3} (- \sqrt[3]{9})$

Step 2.4

Add $1$ and $1$ .

$8 {\sqrt[3]{3}}^{2} + \sqrt[3]{3} (- \sqrt[3]{9})$

Step 3

Multiply $\sqrt[3]{3} (- \sqrt[3]{9})$ .

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Step 3.1

Combine using the product rule for radicals.

$8 {\sqrt[3]{3}}^{2} - \sqrt[3]{3 \cdot 9}$

Step 3.2

Multiply $3$ by $9$ .

$8 {\sqrt[3]{3}}^{2} - \sqrt[3]{27}$

Step 4

Simplify each term.

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Step 4.1

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

$8 \sqrt[3]{3^{2}} - \sqrt[3]{27}$

Step 4.2

Raise $3$ to the power of $2$ .

$8 \sqrt[3]{9} - \sqrt[3]{27}$

Step 4.3

Rewrite $27$ as $3^{3}$ .

$8 \sqrt[3]{9} - \sqrt[3]{3^{3}}$

Step 4.4

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

$8 \sqrt[3]{9} - 1 \cdot 3$

Step 4.5

Multiply $- 1$ by $3$ .

$8 \sqrt[3]{9} - 3$

Step 5

The result can be shown in multiple forms.

Exact Form:

$8 \sqrt[3]{9} - 3$

Decimal Form:

$13.64067058 \dots$