Algebra Examples

$\sqrt[3]{\frac{192 x^{7}}{1029 x^{10}}}$

Step 1

Reduce the expression $\frac{192 x^{7}}{1029 x^{10}}$ by cancelling the common factors.

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Step 1.1

Factor $3$ out of $192 x^{7}$ .

$\sqrt[3]{\frac{3 (64 x^{7})}{1029 x^{10}}}$

Step 1.2

Factor $3$ out of $1029 x^{10}$ .

$\sqrt[3]{\frac{3 (64 x^{7})}{3 (343 x^{10})}}$

Step 1.3

Cancel the common factor.

$\sqrt[3]{\frac{3 (64 x^{7})}{3 (343 x^{10})}}$

Step 1.4

Rewrite the expression.

$\sqrt[3]{\frac{64 x^{7}}{343 x^{10}}}$

Step 2

Cancel the common factor of $x^{7}$ and $x^{10}$ .

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Step 2.1

Factor $x^{7}$ out of $64 x^{7}$ .

$\sqrt[3]{\frac{x^{7} \cdot 64}{343 x^{10}}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $x^{7}$ out of $343 x^{10}$ .

$\sqrt[3]{\frac{x^{7} \cdot 64}{x^{7} (343 x^{3})}}$

Step 2.2.2

Cancel the common factor.

$\sqrt[3]{\frac{x^{7} \cdot 64}{x^{7} (343 x^{3})}}$

Step 2.2.3

Rewrite the expression.

$\sqrt[3]{\frac{64}{343 x^{3}}}$

Step 3

Rewrite $64$ as $4^{3}$ .

$\sqrt[3]{\frac{4^{3}}{343 x^{3}}}$

Step 4

Rewrite $343 x^{3}$ as ${(7 x)}^{3}$ .

$\sqrt[3]{\frac{4^{3}}{{(7 x)}^{3}}}$

Step 5

Rewrite $\frac{4^{3}}{{(7 x)}^{3}}$ as ${(\frac{4}{7 x})}^{3}$ .

$\sqrt[3]{{(\frac{4}{7 x})}^{3}}$

Step 6

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

$\frac{4}{7 x}$