Precalculus Examples

$\log_{3} (x) (\frac{\sqrt[3]{x^{9} y^{5}}}{z^{4}})$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $x^{9} y^{5}$ as ${(x^{3} y)}^{3} y^{2}$ .

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Step 1.1.1

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

$\log_{3} (x) \frac{\sqrt[3]{{(x^{3})}^{3} y^{5}}}{z^{4}}$

Step 1.1.2

Factor out $y^{3}$ .

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

Step 1.1.3

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

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

Step 1.2

Pull terms out from under the radical.

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

Step 2

Combine $\log_{3} (x)$ and $\frac{x^{3} y \sqrt[3]{y^{2}}}{z^{4}}$ .

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

Step 3

Reorder factors in $\frac{\log_{3} (x) x^{3} y \sqrt[3]{y^{2}}}{z^{4}}$ .

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