Algebra Examples

$\frac{\sqrt[4]{16 x^{16} y^{24}}}{\sqrt[4]{x^{2} y^{4}}}$

Step 1

Combine $\sqrt[4]{16 x^{16} y^{24}}$ and $\sqrt[4]{x^{2} y^{4}}$ into a single radical.

$\sqrt[4]{\frac{16 x^{16} y^{24}}{x^{2} y^{4}}}$

Step 2

Reduce the expression $\frac{16 x^{16} y^{24}}{x^{2} y^{4}}$ by cancelling the common factors.

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Step 2.1

Factor $x^{2}$ out of $16 x^{16} y^{24}$ .

$\sqrt[4]{\frac{x^{2} (16 x^{14} y^{24})}{x^{2} y^{4}}}$

Step 2.2

Factor $x^{2}$ out of $x^{2} y^{4}$ .

$\sqrt[4]{\frac{x^{2} (16 x^{14} y^{24})}{x^{2} (y^{4})}}$

Step 2.3

Cancel the common factor.

$\sqrt[4]{\frac{x^{2} (16 x^{14} y^{24})}{x^{2} y^{4}}}$

Step 2.4

Rewrite the expression.

$\sqrt[4]{\frac{16 x^{14} y^{24}}{y^{4}}}$

Step 3

Cancel the common factor of $y^{24}$ and $y^{4}$ .

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Step 3.1

Factor $y^{4}$ out of $16 x^{14} y^{24}$ .

$\sqrt[4]{\frac{y^{4} (16 x^{14} y^{20})}{y^{4}}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Multiply by $1$ .

$\sqrt[4]{\frac{y^{4} (16 x^{14} y^{20})}{y^{4} \cdot 1}}$

Step 3.2.2

Cancel the common factor.

$\sqrt[4]{\frac{y^{4} (16 x^{14} y^{20})}{y^{4} \cdot 1}}$

Step 3.2.3

Rewrite the expression.

$\sqrt[4]{\frac{16 x^{14} y^{20}}{1}}$

Step 3.2.4

Divide $16 x^{14} y^{20}$ by $1$ .

$\sqrt[4]{16 x^{14} y^{20}}$

Step 4

Rewrite $16 x^{14} y^{20}$ as ${(2 x^{3} y^{5})}^{4} x^{2}$ .

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Step 4.1

Rewrite $16$ as $2^{4}$ .

$\sqrt[4]{2^{4} x^{14} y^{20}}$

Step 4.2

Factor out $x^{12}$ .

$\sqrt[4]{2^{4} (x^{12} x^{2}) y^{20}}$

Step 4.3

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

$\sqrt[4]{2^{4} ({(x^{3})}^{4} x^{2}) y^{20}}$

Step 4.4

Rewrite $y^{20}$ as ${(y^{5})}^{4}$ .

$\sqrt[4]{2^{4} ({(x^{3})}^{4} x^{2}) {(y^{5})}^{4}}$

Step 4.5

Move $x^{2}$ .

$\sqrt[4]{2^{4} ({(x^{3})}^{4}) {(y^{5})}^{4} x^{2}}$

Step 4.6

Rewrite $2^{4} ({(x^{3})}^{4}) {(y^{5})}^{4}$ as ${(2 x^{3} y^{5})}^{4}$ .

$\sqrt[4]{{(2 x^{3} y^{5})}^{4} x^{2}}$

Step 5

Pull terms out from under the radical.

$| 2 x^{3} y^{5} | \sqrt[4]{x^{2}}$

Step 6

Remove non-negative terms from the absolute value.

$2 | x^{3} y^{5} | \sqrt[4]{x^{2}}$

Step 7

Rewrite $\sqrt[4]{x^{2}}$ as $\sqrt{\sqrt{x^{2}}}$ .

$2 | x^{3} y^{5} | \sqrt{\sqrt{x^{2}}}$

Step 8

Pull terms out from under the radical.

$2 | x^{3} y^{5} | \sqrt{| x |}$