Precalculus Examples

$\frac{x^{\frac{3}{5}} y^{\frac{9}{10}}}{x^{- \frac{2}{5}} y^{\frac{1}{2}}}$

Step 1

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

$\frac{x^{\frac{3}{5}} y^{\frac{9}{10}} x^{\frac{2}{5}}}{y^{\frac{1}{2}}}$

Step 2

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

$x^{\frac{3}{5}} y^{\frac{9}{10}} x^{\frac{2}{5}} y^{- \frac{1}{2}}$

Step 3

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

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Step 3.1

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

$x^{\frac{2}{5}} x^{\frac{3}{5}} y^{\frac{9}{10}} y^{- \frac{1}{2}}$

Step 3.2

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

$x^{\frac{2}{5} + \frac{3}{5}} y^{\frac{9}{10}} y^{- \frac{1}{2}}$

Step 3.3

Combine the numerators over the common denominator.

$x^{\frac{2 + 3}{5}} y^{\frac{9}{10}} y^{- \frac{1}{2}}$

Step 3.4

Add $2$ and $3$ .

$x^{\frac{5}{5}} y^{\frac{9}{10}} y^{- \frac{1}{2}}$

Step 3.5

Divide $5$ by $5$ .

$x^{1} y^{\frac{9}{10}} y^{- \frac{1}{2}}$

Step 4

Simplify $x^{1} y^{\frac{9}{10}}$ .

$x y^{\frac{9}{10}} y^{- \frac{1}{2}}$

Step 5

Multiply $y^{\frac{9}{10}}$ by $y^{- \frac{1}{2}}$ by adding the exponents.

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Step 5.1

Move $y^{- \frac{1}{2}}$ .

$x (y^{- \frac{1}{2}} y^{\frac{9}{10}})$

Step 5.2

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

$x y^{- \frac{1}{2} + \frac{9}{10}}$

Step 5.3

To write $- \frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$x y^{- \frac{1}{2} \cdot \frac{5}{5} + \frac{9}{10}}$

Step 5.4

Write each expression with a common denominator of $10$ , by multiplying each by an appropriate factor of $1$ .

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Step 5.4.1

Multiply $\frac{1}{2}$ by $\frac{5}{5}$ .

$x y^{- \frac{5}{2 \cdot 5} + \frac{9}{10}}$

Step 5.4.2

Multiply $2$ by $5$ .

$x y^{- \frac{5}{10} + \frac{9}{10}}$

Step 5.5

Combine the numerators over the common denominator.

$x y^{\frac{- 5 + 9}{10}}$

Step 5.6

Add $- 5$ and $9$ .

$x y^{\frac{4}{10}}$

Step 5.7

Cancel the common factor of $4$ and $10$ .

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Step 5.7.1

Factor $2$ out of $4$ .

$x y^{\frac{2 (2)}{10}}$

Step 5.7.2

Cancel the common factors.

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Step 5.7.2.1

Factor $2$ out of $10$ .

$x y^{\frac{2 \cdot 2}{2 \cdot 5}}$

Step 5.7.2.2

Cancel the common factor.

$x y^{\frac{2 \cdot 2}{2 \cdot 5}}$

Step 5.7.2.3

Rewrite the expression.

$x y^{\frac{2}{5}}$