Algebra Examples

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

Step 1

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

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

Step 2

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

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

Step 3

Simplify the numerator.

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Step 3.1

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

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Step 3.1.1

Move $x^{\frac{1}{3}}$ .

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

Step 3.1.2

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

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Step 3.1.2.1

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

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

Step 3.1.2.2

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

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

Step 3.1.3

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

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

Step 3.1.4

Combine the numerators over the common denominator.

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

Step 3.1.5

Add $1$ and $3$ .

$\frac{4 x^{\frac{4}{3}} y^{- 2} y^{5}}{12}$

Step 3.2

Multiply $y^{- 2}$ by $y^{5}$ by adding the exponents.

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Step 3.2.1

Move $y^{5}$ .

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

Step 3.2.2

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

$\frac{4 x^{\frac{4}{3}} y^{5 - 2}}{12}$

Step 3.2.3

Subtract $2$ from $5$ .

$\frac{4 x^{\frac{4}{3}} y^{3}}{12}$

Step 4

Factor $4$ out of $4 x^{\frac{4}{3}} y^{3}$ .

$\frac{4 (x^{\frac{4}{3}} y^{3})}{12}$

Step 5

Cancel the common factors.

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Step 5.1

Factor $4$ out of $12$ .

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

Step 5.2

Cancel the common factor.

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

Step 5.3

Rewrite the expression.

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

Step 6

Reorder factors in $\frac{x^{\frac{4}{3}} y^{3}}{3}$ .

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