Basic Math Examples

$\frac{x^{\frac{2}{5}} y^{- \frac{1}{4}}}{{(4 x^{- 1} y)}^{3}}$

Step 1

Move $y^{- \frac{1}{4}}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{x^{\frac{2}{5}}}{{(4 x^{- 1} y)}^{3} y^{\frac{1}{4}}}$

Step 2

Simplify the denominator.

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Step 2.1

Apply the product rule to $4 x^{- 1} y$ .

$\frac{x^{\frac{2}{5}}}{{(4 x^{- 1})}^{3} y^{3} y^{\frac{1}{4}}}$

Step 2.2

Multiply $y^{3}$ by $y^{\frac{1}{4}}$ by adding the exponents.

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Step 2.2.1

Move $y^{\frac{1}{4}}$ .

$\frac{x^{\frac{2}{5}}}{{(4 x^{- 1})}^{3} (y^{\frac{1}{4}} y^{3})}$

Step 2.2.2

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

$\frac{x^{\frac{2}{5}}}{{(4 x^{- 1})}^{3} y^{\frac{1}{4} + 3}}$

Step 2.2.3

To write $3$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{x^{\frac{2}{5}}}{{(4 x^{- 1})}^{3} y^{\frac{1}{4} + 3 \cdot \frac{4}{4}}}$

Step 2.2.4

Combine $3$ and $\frac{4}{4}$ .

$\frac{x^{\frac{2}{5}}}{{(4 x^{- 1})}^{3} y^{\frac{1}{4} + \frac{3 \cdot 4}{4}}}$

Step 2.2.5

Combine the numerators over the common denominator.

$\frac{x^{\frac{2}{5}}}{{(4 x^{- 1})}^{3} y^{\frac{1 + 3 \cdot 4}{4}}}$

Step 2.2.6

Simplify the numerator.

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Step 2.2.6.1

Multiply $3$ by $4$ .

$\frac{x^{\frac{2}{5}}}{{(4 x^{- 1})}^{3} y^{\frac{1 + 12}{4}}}$

Step 2.2.6.2

Add $1$ and $12$ .

$\frac{x^{\frac{2}{5}}}{{(4 x^{- 1})}^{3} y^{\frac{13}{4}}}$

Step 2.3

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{x^{\frac{2}{5}}}{{(4 \frac{1}{x})}^{3} y^{\frac{13}{4}}}$

Step 2.4

Combine $4$ and $\frac{1}{x}$ .

$\frac{x^{\frac{2}{5}}}{{(\frac{4}{x})}^{3} y^{\frac{13}{4}}}$

Step 2.5

Apply the product rule to $\frac{4}{x}$ .

$\frac{x^{\frac{2}{5}}}{\frac{4^{3}}{x^{3}} y^{\frac{13}{4}}}$

Step 2.6

Raise $4$ to the power of $3$ .

$\frac{x^{\frac{2}{5}}}{\frac{64}{x^{3}} y^{\frac{13}{4}}}$

Step 3

Combine $\frac{64}{x^{3}}$ and $y^{\frac{13}{4}}$ .

$\frac{x^{\frac{2}{5}}}{\frac{64 y^{\frac{13}{4}}}{x^{3}}}$

Step 4

Multiply the numerator by the reciprocal of the denominator.

$x^{\frac{2}{5}} \frac{x^{3}}{64 y^{\frac{13}{4}}}$

Step 5

Multiply $x^{\frac{2}{5}} \frac{x^{3}}{64 y^{\frac{13}{4}}}$ .

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Step 5.1

Combine $x^{\frac{2}{5}}$ and $\frac{x^{3}}{64 y^{\frac{13}{4}}}$ .

$\frac{x^{\frac{2}{5}} x^{3}}{64 y^{\frac{13}{4}}}$

Step 5.2

Multiply $x^{\frac{2}{5}}$ by $x^{3}$ by adding the exponents.

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Step 5.2.1

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

$\frac{x^{\frac{2}{5} + 3}}{64 y^{\frac{13}{4}}}$

Step 5.2.2

To write $3$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$\frac{x^{\frac{2}{5} + 3 \cdot \frac{5}{5}}}{64 y^{\frac{13}{4}}}$

Step 5.2.3

Combine $3$ and $\frac{5}{5}$ .

$\frac{x^{\frac{2}{5} + \frac{3 \cdot 5}{5}}}{64 y^{\frac{13}{4}}}$

Step 5.2.4

Combine the numerators over the common denominator.

$\frac{x^{\frac{2 + 3 \cdot 5}{5}}}{64 y^{\frac{13}{4}}}$

Step 5.2.5

Simplify the numerator.

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Step 5.2.5.1

Multiply $3$ by $5$ .

$\frac{x^{\frac{2 + 15}{5}}}{64 y^{\frac{13}{4}}}$

Step 5.2.5.2

Add $2$ and $15$ .

$\frac{x^{\frac{17}{5}}}{64 y^{\frac{13}{4}}}$