Algebra Examples

$\frac{x^{\frac{2}{5}} y}{x y^{- \frac{1}{3}}}$

Step 1

Move $x^{\frac{2}{5}}$ to the denominator using the negative exponent rule $b^{n} = \frac{1}{b^{- n}}$ .

$\frac{y}{x y^{- \frac{1}{3}} x^{- \frac{2}{5}}}$

Step 2

Multiply $x$ by $x^{- \frac{2}{5}}$ by adding the exponents.

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Step 2.1

Move $x^{- \frac{2}{5}}$ .

$\frac{y}{x^{- \frac{2}{5}} x y^{- \frac{1}{3}}}$

Step 2.2

Multiply $x^{- \frac{2}{5}}$ by $x$ .

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Step 2.2.1

Raise $x$ to the power of $1$ .

$\frac{y}{x^{- \frac{2}{5}} x^{1} y^{- \frac{1}{3}}}$

Step 2.2.2

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

$\frac{y}{x^{- \frac{2}{5} + 1} y^{- \frac{1}{3}}}$

Step 2.3

Write $1$ as a fraction with a common denominator.

$\frac{y}{x^{- \frac{2}{5} + \frac{5}{5}} y^{- \frac{1}{3}}}$

Step 2.4

Combine the numerators over the common denominator.

$\frac{y}{x^{\frac{- 2 + 5}{5}} y^{- \frac{1}{3}}}$

Step 2.5

Add $- 2$ and $5$ .

$\frac{y}{x^{\frac{3}{5}} y^{- \frac{1}{3}}}$

Step 3

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

$\frac{y \cdot y^{\frac{1}{3}}}{x^{\frac{3}{5}}}$

Step 4

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

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Step 4.1

Multiply $y$ by $y^{\frac{1}{3}}$ .

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Step 4.1.1

Raise $y$ to the power of $1$ .

$\frac{y^{1} y^{\frac{1}{3}}}{x^{\frac{3}{5}}}$

Step 4.1.2

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

$\frac{y^{1 + \frac{1}{3}}}{x^{\frac{3}{5}}}$

Step 4.2

Write $1$ as a fraction with a common denominator.

$\frac{y^{\frac{3}{3} + \frac{1}{3}}}{x^{\frac{3}{5}}}$

Step 4.3

Combine the numerators over the common denominator.

$\frac{y^{\frac{3 + 1}{3}}}{x^{\frac{3}{5}}}$

Step 4.4

Add $3$ and $1$ .

$\frac{y^{\frac{4}{3}}}{x^{\frac{3}{5}}}$