Algebra Examples

$\sqrt[3]{s^{2} t^{4}} \cdot \sqrt[3]{s^{4} t^{6}}$

Step 1

Rewrite $s^{2} t^{4}$ as $t^{3} (s^{2} t)$ .

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Step 1.1

Factor out $t^{3}$ .

$\sqrt[3]{s^{2} (t^{3} t)} \cdot \sqrt[3]{s^{4} t^{6}}$

Step 1.2

Reorder $s^{2}$ and $t^{3}$ .

$\sqrt[3]{t^{3} s^{2} t} \cdot \sqrt[3]{s^{4} t^{6}}$

Step 1.3

Add parentheses.

$\sqrt[3]{t^{3} (s^{2} t)} \cdot \sqrt[3]{s^{4} t^{6}}$

Step 2

Pull terms out from under the radical.

$t \sqrt[3]{s^{2} t} \cdot \sqrt[3]{s^{4} t^{6}}$

Step 3

Rewrite $s^{4} t^{6}$ as ${(s t^{2})}^{3} s$ .

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Step 3.1

Factor out $s^{3}$ .

$t \sqrt[3]{s^{2} t} \cdot \sqrt[3]{s^{3} s t^{6}}$

Step 3.2

Rewrite $t^{6}$ as ${(t^{2})}^{3}$ .

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

Step 3.3

Move $s$ .

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

Step 3.4

Rewrite $s^{3} {(t^{2})}^{3}$ as ${(s t^{2})}^{3}$ .

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

Step 4

Pull terms out from under the radical.

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

Step 5

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

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Step 5.1

Move $t^{2}$ .

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

Step 5.2

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

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Step 5.2.1

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

$t^{2} t^{1} \sqrt[3]{s^{2} t} \cdot (s \sqrt[3]{s})$

Step 5.2.2

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

$t^{2 + 1} \sqrt[3]{s^{2} t} \cdot (s \sqrt[3]{s})$

Step 5.3

Add $2$ and $1$ .

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

Step 6

Multiply $t^{3} \sqrt[3]{s^{2} t} (s \sqrt[3]{s})$ .

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Step 6.1

Combine using the product rule for radicals.

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

Step 6.2

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

$t^{3} (s \sqrt[3]{s^{1} s^{2} t})$

Step 6.3

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

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

Step 6.4

Add $1$ and $2$ .

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

Step 7

Pull terms out from under the radical.

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

Step 8

Multiply $s$ by $s$ by adding the exponents.

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Step 8.1

Move $s$ .

$t^{3} (s \cdot s \sqrt[3]{t})$

Step 8.2

Multiply $s$ by $s$ .

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

Step 9

Reorder factors in $t^{3} (s^{2} \sqrt[3]{t})$ .

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