Basic Math Examples

$\sqrt[3]{6 y z^{2}} \cdot \sqrt[3]{12 y^{4} z^{7}}$

Step 1

Rewrite $12 y^{4} z^{7}$ as ${(y z^{2})}^{3} \cdot (12 y z)$ .

Tap for more steps...

Step 1.1

Factor out $y^{3}$ .

$\sqrt[3]{6 y z^{2}} \cdot \sqrt[3]{12 (y^{3} y) z^{7}}$

Step 1.2

Factor out $z^{6}$ .

$\sqrt[3]{6 y z^{2}} \cdot \sqrt[3]{12 (y^{3} y) (z^{6} z)}$

Step 1.3

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

$\sqrt[3]{6 y z^{2}} \cdot \sqrt[3]{12 (y^{3} y) ({(z^{2})}^{3} z)}$

Step 1.4

Move $y$ .

$\sqrt[3]{6 y z^{2}} \cdot \sqrt[3]{12 (y^{3}) {(z^{2})}^{3} y z}$

Step 1.5

Move $12$ .

$\sqrt[3]{6 y z^{2}} \cdot \sqrt[3]{y^{3} {(z^{2})}^{3} \cdot 12 y z}$

Step 1.6

Rewrite $(y^{3}) {(z^{2})}^{3}$ as ${(y z^{2})}^{3}$ .

$\sqrt[3]{6 y z^{2}} \cdot \sqrt[3]{{(y z^{2})}^{3} \cdot 12 y z}$

Step 1.7

Add parentheses.

$\sqrt[3]{6 y z^{2}} \cdot \sqrt[3]{{(y z^{2})}^{3} \cdot 12 (y z)}$

Step 1.8

Add parentheses.

$\sqrt[3]{6 y z^{2}} \cdot \sqrt[3]{{(y z^{2})}^{3} \cdot (12 y z)}$

Step 2

Pull terms out from under the radical.

$\sqrt[3]{6 y z^{2}} \cdot (y z^{2} \sqrt[3]{12 y z})$

Step 3

Multiply $\sqrt[3]{6 y z^{2}} (y z^{2} \sqrt[3]{12 y z})$ .

Tap for more steps...

Step 3.1

Combine using the product rule for radicals.

$y z^{2} \sqrt[3]{6 y z^{2} (12 y z)}$

Step 3.2

Multiply $12$ by $6$ .

$y z^{2} \sqrt[3]{72 y z^{2} (y z)}$

Step 3.3

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

$y z^{2} \sqrt[3]{72 (y^{1} y) z^{2} z}$

Step 3.4

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

$y z^{2} \sqrt[3]{72 (y^{1} y^{1}) z^{2} z}$

Step 3.5

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

$y z^{2} \sqrt[3]{72 y^{1 + 1} z^{2} z}$

Step 3.6

Add $1$ and $1$ .

$y z^{2} \sqrt[3]{72 y^{2} z^{2} z}$

Step 3.7

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

$y z^{2} \sqrt[3]{72 y^{2} (z^{1} z^{2})}$

Step 3.8

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

$y z^{2} \sqrt[3]{72 y^{2} z^{1 + 2}}$

Step 3.9

Add $1$ and $2$ .

$y z^{2} \sqrt[3]{72 y^{2} z^{3}}$

Step 4

Rewrite $72 y^{2} z^{3}$ as ${(2 z)}^{3} \cdot (9 y^{2})$ .

Tap for more steps...

Step 4.1

Factor $8$ out of $72$ .

$y z^{2} \sqrt[3]{8 (9) y^{2} z^{3}}$

Step 4.2

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

$y z^{2} \sqrt[3]{2^{3} \cdot 9 y^{2} z^{3}}$

Step 4.3

Move $y^{2}$ .

$y z^{2} \sqrt[3]{2^{3} \cdot 9 z^{3} y^{2}}$

Step 4.4

Move $9$ .

$y z^{2} \sqrt[3]{2^{3} z^{3} \cdot 9 y^{2}}$

Step 4.5

Rewrite $2^{3} z^{3}$ as ${(2 z)}^{3}$ .

$y z^{2} \sqrt[3]{{(2 z)}^{3} \cdot 9 y^{2}}$

Step 4.6

Add parentheses.

$y z^{2} \sqrt[3]{{(2 z)}^{3} \cdot (9 y^{2})}$

Step 5

Pull terms out from under the radical.

$y z^{2} (2 z \sqrt[3]{9 y^{2}})$

Step 6

Rewrite using the commutative property of multiplication.

$2 y z^{2} (z \sqrt[3]{9 y^{2}})$

Step 7

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

Tap for more steps...

Step 7.1

Move $z$ .

$2 y (z \cdot z^{2}) \sqrt[3]{9 y^{2}}$

Step 7.2

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

Tap for more steps...

Step 7.2.1

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

$2 y (z^{1} z^{2}) \sqrt[3]{9 y^{2}}$

Step 7.2.2

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

$2 y z^{1 + 2} \sqrt[3]{9 y^{2}}$

Step 7.3

Add $1$ and $2$ .

$2 y z^{3} \sqrt[3]{9 y^{2}}$