Precalculus Examples

$\log_{5} (\sqrt[3]{x^{2} y} - 25)$

Step 1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{x^{2} y}$ as ${(x^{2} y)}^{\frac{1}{3}}$ .

$\log_{5} ({(x^{2} y)}^{\frac{1}{3}} - 25)$

Step 2

Simplify each term.

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Step 2.1

Apply the product rule to $x^{2} y$ .

$\log_{5} ({(x^{2})}^{\frac{1}{3}} y^{\frac{1}{3}} - 25)$

Step 2.2

Multiply the exponents in ${(x^{2})}^{\frac{1}{3}}$ .

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Step 2.2.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$\log_{5} (x^{2 (\frac{1}{3})} y^{\frac{1}{3}} - 25)$

Step 2.2.2

Combine $2$ and $\frac{1}{3}$ .

$\log_{5} (x^{\frac{2}{3}} y^{\frac{1}{3}} - 25)$