Precalculus Examples

$\sqrt[3]{8 x^{7} y^{9} z^{3}}$

Rewrite $8 x^{7} y^{9} z^{3}$ as ${(2 x^{2} y^{3} z)}^{3} x$ .

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

$\sqrt[3]{2^{3} x^{7} y^{9} z^{3}}$

Factor out $x^{6}$ .

$\sqrt[3]{2^{3} (x^{6} x) y^{9} z^{3}}$

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

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

Rewrite $y^{9}$ as ${(y^{3})}^{3}$ .

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

Move $x$ .

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

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

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

Pull terms out from under the radical.

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