Precalculus Examples

$\frac{x^{\frac{4}{3}} y^{- \frac{2}{3}}}{{(x^{2} y)}^{\frac{1}{3}}}$

Step 1

Move $y^{- \frac{2}{3}}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{x^{\frac{4}{3}}}{{(x^{2} y)}^{\frac{1}{3}} y^{\frac{2}{3}}}$

Step 2

Simplify the denominator.

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Step 2.1

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

$\frac{x^{\frac{4}{3}}}{{(x^{2})}^{\frac{1}{3}} y^{\frac{1}{3}} y^{\frac{2}{3}}}$

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, ${(a^{m})}^{n} = a^{m n}$ .

$\frac{x^{\frac{4}{3}}}{x^{2 (\frac{1}{3})} y^{\frac{1}{3}} y^{\frac{2}{3}}}$

Step 2.2.2

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

$\frac{x^{\frac{4}{3}}}{x^{\frac{2}{3}} y^{\frac{1}{3}} y^{\frac{2}{3}}}$

Step 2.3

Combine exponents.

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Step 2.3.1

Multiply $y^{\frac{1}{3}}$ by $y^{\frac{2}{3}}$ by adding the exponents.

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Step 2.3.1.1

Move $y^{\frac{2}{3}}$ .

$\frac{x^{\frac{4}{3}}}{x^{\frac{2}{3}} (y^{\frac{2}{3}} y^{\frac{1}{3}})}$

Step 2.3.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{x^{\frac{4}{3}}}{x^{\frac{2}{3}} y^{\frac{2}{3} + \frac{1}{3}}}$

Step 2.3.1.3

Combine the numerators over the common denominator.

$\frac{x^{\frac{4}{3}}}{x^{\frac{2}{3}} y^{\frac{2 + 1}{3}}}$

Step 2.3.1.4

Add $2$ and $1$ .

$\frac{x^{\frac{4}{3}}}{x^{\frac{2}{3}} y^{\frac{3}{3}}}$

Step 2.3.1.5

Divide $3$ by $3$ .

$\frac{x^{\frac{4}{3}}}{x^{\frac{2}{3}} y^{1}}$

Step 2.3.2

Simplify $x^{\frac{2}{3}} y^{1}$ .

$\frac{x^{\frac{4}{3}}}{x^{\frac{2}{3}} y}$

Step 3

Move $x^{\frac{2}{3}}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$\frac{x^{\frac{4}{3}} x^{- \frac{2}{3}}}{y}$

Step 4

Multiply $x^{\frac{4}{3}}$ by $x^{- \frac{2}{3}}$ by adding the exponents.

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Step 4.1

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{x^{\frac{4}{3} - \frac{2}{3}}}{y}$

Step 4.2

Combine the numerators over the common denominator.

$\frac{x^{\frac{4 - 2}{3}}}{y}$

Step 4.3

Subtract $2$ from $4$ .

$\frac{x^{\frac{2}{3}}}{y}$