Algebra Examples

$x^{- \frac{4}{3}} y^{- 1} \sqrt[3]{8 x^{5} y^{5}}$

Step 1

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

$\frac{1}{x^{\frac{4}{3}}} y^{- 1} \sqrt[3]{8 x^{5} y^{5}}$

Step 2

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

$\frac{1}{x^{\frac{4}{3}}} \cdot \frac{1}{y} \sqrt[3]{8 x^{5} y^{5}}$

Step 3

Combine.

$\frac{1 \cdot 1}{x^{\frac{4}{3}} y} \sqrt[3]{8 x^{5} y^{5}}$

Step 4

Multiply $1$ by $1$ .

$\frac{1}{x^{\frac{4}{3}} y} \sqrt[3]{8 x^{5} y^{5}}$

Step 5

Rewrite $8 x^{5} y^{5}$ as ${(2 x y)}^{3} (x^{2} y^{2})$ .

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Step 5.1

Rewrite $8$ as $2^{3}$ .

$\frac{1}{x^{\frac{4}{3}} y} \sqrt[3]{2^{3} x^{5} y^{5}}$

Step 5.2

Factor out $x^{3}$ .

$\frac{1}{x^{\frac{4}{3}} y} \sqrt[3]{2^{3} (x^{3} x^{2}) y^{5}}$

Step 5.3

Factor out $y^{3}$ .

$\frac{1}{x^{\frac{4}{3}} y} \sqrt[3]{2^{3} (x^{3} x^{2}) (y^{3} y^{2})}$

Step 5.4

Move $x^{2}$ .

$\frac{1}{x^{\frac{4}{3}} y} \sqrt[3]{2^{3} (x^{3}) y^{3} x^{2} y^{2}}$

Step 5.5

Rewrite $2^{3} (x^{3}) y^{3}$ as ${(2 x y)}^{3}$ .

$\frac{1}{x^{\frac{4}{3}} y} \sqrt[3]{{(2 x y)}^{3} x^{2} y^{2}}$

Step 5.6

Add parentheses.

$\frac{1}{x^{\frac{4}{3}} y} \sqrt[3]{{(2 x y)}^{3} (x^{2} y^{2})}$

Step 6

Pull terms out from under the radical.

$\frac{1}{x^{\frac{4}{3}} y} (2 x y \sqrt[3]{x^{2} y^{2}})$

Step 7

Rewrite using the commutative property of multiplication.

$2 \frac{1}{x^{\frac{4}{3}} y} (x y \sqrt[3]{x^{2} y^{2}})$

Step 8

Combine $2$ and $\frac{1}{x^{\frac{4}{3}} y}$ .

$\frac{2}{x^{\frac{4}{3}} y} (x y \sqrt[3]{x^{2} y^{2}})$

Step 9

Cancel the common factor of $y$ .

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Step 9.1

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

$\frac{2}{y x^{\frac{4}{3}}} (x y \sqrt[3]{x^{2} y^{2}})$

Step 9.2

Factor $y$ out of $x y \sqrt[3]{x^{2} y^{2}}$ .

$\frac{2}{y x^{\frac{4}{3}}} (y (x \sqrt[3]{x^{2} y^{2}}))$

Step 9.3

Cancel the common factor.

$\frac{2}{y x^{\frac{4}{3}}} (y (x \sqrt[3]{x^{2} y^{2}}))$

Step 9.4

Rewrite the expression.

$\frac{2}{x^{\frac{4}{3}}} (x \sqrt[3]{x^{2} y^{2}})$

Step 10

Combine $x$ and $\frac{2}{x^{\frac{4}{3}}}$ .

$\frac{x \cdot 2}{x^{\frac{4}{3}}} \sqrt[3]{x^{2} y^{2}}$

Step 11

Combine $\frac{x \cdot 2}{x^{\frac{4}{3}}}$ and $\sqrt[3]{x^{2} y^{2}}$ .

$\frac{x \cdot 2 \sqrt[3]{x^{2} y^{2}}}{x^{\frac{4}{3}}}$

Step 12

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

$\frac{2 \sqrt[3]{x^{2} y^{2}}}{x^{\frac{4}{3}} x^{- 1}}$

Step 13

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

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Step 13.1

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

$\frac{2 \sqrt[3]{x^{2} y^{2}}}{x^{\frac{4}{3} - 1}}$

Step 13.2

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{2 \sqrt[3]{x^{2} y^{2}}}{x^{\frac{4}{3} - 1 \cdot \frac{3}{3}}}$

Step 13.3

Combine $- 1$ and $\frac{3}{3}$ .

$\frac{2 \sqrt[3]{x^{2} y^{2}}}{x^{\frac{4}{3} + \frac{- 1 \cdot 3}{3}}}$

Step 13.4

Combine the numerators over the common denominator.

$\frac{2 \sqrt[3]{x^{2} y^{2}}}{x^{\frac{4 - 1 \cdot 3}{3}}}$

Step 13.5

Simplify the numerator.

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Step 13.5.1

Multiply $- 1$ by $3$ .

$\frac{2 \sqrt[3]{x^{2} y^{2}}}{x^{\frac{4 - 3}{3}}}$

Step 13.5.2

Subtract $3$ from $4$ .

$\frac{2 \sqrt[3]{x^{2} y^{2}}}{x^{\frac{1}{3}}}$