Algebra Examples

$\sqrt[4]{121 x^{2} y^{3} z^{4}} \sqrt[4]{121 x^{6} y z^{12}}$

Step 1

Rewrite $121 x^{2} y^{3} z^{4}$ as $z^{4} \cdot (121 x^{2} y^{3})$ .

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Step 1.1

Move $y^{3}$ .

$\sqrt[4]{121 x^{2} z^{4} y^{3}} \sqrt[4]{121 x^{6} y z^{12}}$

Step 1.2

Move $x^{2}$ .

$\sqrt[4]{121 z^{4} x^{2} y^{3}} \sqrt[4]{121 x^{6} y z^{12}}$

Step 1.3

Reorder $121$ and $z^{4}$ .

$\sqrt[4]{z^{4} \cdot 121 x^{2} y^{3}} \sqrt[4]{121 x^{6} y z^{12}}$

Step 1.4

Add parentheses.

$\sqrt[4]{z^{4} \cdot 121 (x^{2} y^{3})} \sqrt[4]{121 x^{6} y z^{12}}$

Step 1.5

Add parentheses.

$\sqrt[4]{z^{4} \cdot (121 x^{2} y^{3})} \sqrt[4]{121 x^{6} y z^{12}}$

Step 2

Pull terms out from under the radical.

$z \sqrt[4]{121 x^{2} y^{3}} \sqrt[4]{121 x^{6} y z^{12}}$

Step 3

Rewrite $121 x^{6} y z^{12}$ as ${(x z^{3})}^{4} \cdot (121 x^{2} y)$ .

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Step 3.1

Factor out $x^{4}$ .

$z \sqrt[4]{121 x^{2} y^{3}} \sqrt[4]{121 (x^{4} x^{2}) y z^{12}}$

Step 3.2

Rewrite $z^{12}$ as ${(z^{3})}^{4}$ .

$z \sqrt[4]{121 x^{2} y^{3}} \sqrt[4]{121 (x^{4} x^{2}) y {(z^{3})}^{4}}$

Step 3.3

Move $y$ .

$z \sqrt[4]{121 x^{2} y^{3}} \sqrt[4]{121 (x^{4} x^{2}) {(z^{3})}^{4} y}$

Step 3.4

Move $x^{2}$ .

$z \sqrt[4]{121 x^{2} y^{3}} \sqrt[4]{121 (x^{4}) {(z^{3})}^{4} x^{2} y}$

Step 3.5

Move $121$ .

$z \sqrt[4]{121 x^{2} y^{3}} \sqrt[4]{x^{4} {(z^{3})}^{4} \cdot 121 x^{2} y}$

Step 3.6

Rewrite $(x^{4}) {(z^{3})}^{4}$ as ${(x z^{3})}^{4}$ .

$z \sqrt[4]{121 x^{2} y^{3}} \sqrt[4]{{(x z^{3})}^{4} \cdot 121 x^{2} y}$

Step 3.7

Add parentheses.

$z \sqrt[4]{121 x^{2} y^{3}} \sqrt[4]{{(x z^{3})}^{4} \cdot 121 (x^{2} y)}$

Step 3.8

Add parentheses.

$z \sqrt[4]{121 x^{2} y^{3}} \sqrt[4]{{(x z^{3})}^{4} \cdot (121 x^{2} y)}$

Step 4

Pull terms out from under the radical.

$z \sqrt[4]{121 x^{2} y^{3}} (x z^{3} \sqrt[4]{121 x^{2} y})$

Step 5

Multiply $z$ by $z^{3}$ by adding the exponents.

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Step 5.1

Move $z^{3}$ .

$z^{3} z \sqrt[4]{121 x^{2} y^{3}} (x \sqrt[4]{121 x^{2} y})$

Step 5.2

Multiply $z^{3}$ by $z$ .

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Step 5.2.1

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

$z^{3} z^{1} \sqrt[4]{121 x^{2} y^{3}} (x \sqrt[4]{121 x^{2} y})$

Step 5.2.2

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

$z^{3 + 1} \sqrt[4]{121 x^{2} y^{3}} (x \sqrt[4]{121 x^{2} y})$

Step 5.3

Add $3$ and $1$ .

$z^{4} \sqrt[4]{121 x^{2} y^{3}} (x \sqrt[4]{121 x^{2} y})$

Step 6

Multiply $z^{4} \sqrt[4]{121 x^{2} y^{3}} (x \sqrt[4]{121 x^{2} y})$ .

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Step 6.1

Combine using the product rule for radicals.

$z^{4} (x \sqrt[4]{121 x^{2} y^{3} (121 x^{2} y)})$

Step 6.2

Multiply $121$ by $121$ .

$z^{4} (x \sqrt[4]{14641 x^{2} y^{3} (x^{2} y)})$

Step 6.3

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

$z^{4} (x \sqrt[4]{14641 x^{2 + 2} y^{3} y})$

Step 6.4

Add $2$ and $2$ .

$z^{4} (x \sqrt[4]{14641 x^{4} y^{3} y})$

Step 6.5

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

$z^{4} (x \sqrt[4]{14641 x^{4} (y^{1} y^{3})})$

Step 6.6

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

$z^{4} (x \sqrt[4]{14641 x^{4} y^{1 + 3}})$

Step 6.7

Add $1$ and $3$ .

$z^{4} (x \sqrt[4]{14641 x^{4} y^{4}})$

Step 7

Rewrite $14641 x^{4} y^{4}$ as ${(11 x y)}^{4}$ .

$z^{4} (x \sqrt[4]{{(11 x y)}^{4}})$

Step 8

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

$z^{4} (x (11 x y))$

Step 9

Rewrite using the commutative property of multiplication.

$11 z^{4} x \cdot x y$

Step 10

Multiply $x$ by $x$ by adding the exponents.

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Step 10.1

Move $x$ .

$11 z^{4} (x \cdot x) y$

Step 10.2

Multiply $x$ by $x$ .

$11 z^{4} x^{2} y$