Basic Math Examples

$\frac{x^{\frac{5}{6}} y^{\frac{11}{12}}}{x^{- \frac{1}{6}} y^{\frac{1}{2}}}$

Step 1

Move $x^{- \frac{1}{6}}$ to the numerator using the negative exponent rule $\frac{1}{b^{- n}} = b^{n}$ .

$\frac{x^{\frac{5}{6}} y^{\frac{11}{12}} x^{\frac{1}{6}}}{y^{\frac{1}{2}}}$

Step 2

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

$x^{\frac{5}{6}} y^{\frac{11}{12}} x^{\frac{1}{6}} y^{- \frac{1}{2}}$

Step 3

Multiply $x^{\frac{5}{6}}$ by $x^{\frac{1}{6}}$ by adding the exponents.

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Step 3.1

Move $x^{\frac{1}{6}}$ .

$x^{\frac{1}{6}} x^{\frac{5}{6}} y^{\frac{11}{12}} y^{- \frac{1}{2}}$

Step 3.2

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

$x^{\frac{1}{6} + \frac{5}{6}} y^{\frac{11}{12}} y^{- \frac{1}{2}}$

Step 3.3

Combine the numerators over the common denominator.

$x^{\frac{1 + 5}{6}} y^{\frac{11}{12}} y^{- \frac{1}{2}}$

Step 3.4

Add $1$ and $5$ .

$x^{\frac{6}{6}} y^{\frac{11}{12}} y^{- \frac{1}{2}}$

Step 3.5

Divide $6$ by $6$ .

$x^{1} y^{\frac{11}{12}} y^{- \frac{1}{2}}$

Step 4

Simplify $x^{1} y^{\frac{11}{12}}$ .

$x y^{\frac{11}{12}} y^{- \frac{1}{2}}$

Step 5

Multiply $y^{\frac{11}{12}}$ by $y^{- \frac{1}{2}}$ by adding the exponents.

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Step 5.1

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

$x (y^{- \frac{1}{2}} y^{\frac{11}{12}})$

Step 5.2

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

$x y^{- \frac{1}{2} + \frac{11}{12}}$

Step 5.3

To write $- \frac{1}{2}$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$x y^{- \frac{1}{2} \cdot \frac{6}{6} + \frac{11}{12}}$

Step 5.4

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

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Step 5.4.1

Multiply $\frac{1}{2}$ by $\frac{6}{6}$ .

$x y^{- \frac{6}{2 \cdot 6} + \frac{11}{12}}$

Step 5.4.2

Multiply $2$ by $6$ .

$x y^{- \frac{6}{12} + \frac{11}{12}}$

Step 5.5

Combine the numerators over the common denominator.

$x y^{\frac{- 6 + 11}{12}}$

Step 5.6

Add $- 6$ and $11$ .

$x y^{\frac{5}{12}}$