Basic Math Examples

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

Step 1

Apply the distributive property.

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

Step 2

Multiply $\sqrt[3]{3 t} \sqrt[3]{9 t}$ .

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Step 2.1

Combine using the product rule for radicals.

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

Step 2.2

Multiply $9$ by $3$ .

$\sqrt[3]{27 t \cdot t} + \sqrt[3]{3 t} (- \sqrt[3]{t^{2}})$

Step 2.3

Raise $t$ to the power of $1$ .

$\sqrt[3]{27 (t^{1} t)} + \sqrt[3]{3 t} (- \sqrt[3]{t^{2}})$

Step 2.4

Raise $t$ to the power of $1$ .

$\sqrt[3]{27 (t^{1} t^{1})} + \sqrt[3]{3 t} (- \sqrt[3]{t^{2}})$

Step 2.5

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

$\sqrt[3]{27 t^{1 + 1}} + \sqrt[3]{3 t} (- \sqrt[3]{t^{2}})$

Step 2.6

Add $1$ and $1$ .

$\sqrt[3]{27 t^{2}} + \sqrt[3]{3 t} (- \sqrt[3]{t^{2}})$

Step 3

Rewrite using the commutative property of multiplication.

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

Step 4

Simplify each term.

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Step 4.1

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

$\sqrt[3]{3^{3} t^{2}} - \sqrt[3]{3 t} \sqrt[3]{t^{2}}$

Step 4.2

Pull terms out from under the radical.

$3 \sqrt[3]{t^{2}} - \sqrt[3]{3 t} \sqrt[3]{t^{2}}$

Step 4.3

Multiply $- \sqrt[3]{3 t} \sqrt[3]{t^{2}}$ .

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Step 4.3.1

Combine using the product rule for radicals.

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

Step 4.3.2

Multiply $t^{2}$ by $t$ by adding the exponents.

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Step 4.3.2.1

Move $t$ .

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

Step 4.3.2.2

Multiply $t$ by $t^{2}$ .

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Step 4.3.2.2.1

Raise $t$ to the power of $1$ .

$3 \sqrt[3]{t^{2}} - \sqrt[3]{t^{1} t^{2} \cdot 3}$

Step 4.3.2.2.2

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

$3 \sqrt[3]{t^{2}} - \sqrt[3]{t^{1 + 2} \cdot 3}$

Step 4.3.2.3

Add $1$ and $2$ .

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

Step 4.4

Pull terms out from under the radical.

$3 \sqrt[3]{t^{2}} - t \sqrt[3]{3}$