Algebra Examples

3 x^{- 2} y^{\frac{1}{2}} \sqrt[3]{8 x^{4} y}

$3 x^{- 2} y^{\frac{1}{2}} \sqrt[3]{8 x^{4} y}$

Step 1

Rewrite the expression using the negative exponent rule

b^{- n} = \frac{1}{b^{n}}

$b^{- n} = \frac{1}{b^{n}}$ .

3 \frac{1}{x^{2}} y^{\frac{1}{2}} \sqrt[3]{8 x^{4} y}

$3 \frac{1}{x^{2}} y^{\frac{1}{2}} \sqrt[3]{8 x^{4} y}$

Step 2

Combine

3

$3$ and

\frac{1}{x^{2}}

$\frac{1}{x^{2}}$ .

\frac{3}{x^{2}} y^{\frac{1}{2}} \sqrt[3]{8 x^{4} y}

$\frac{3}{x^{2}} y^{\frac{1}{2}} \sqrt[3]{8 x^{4} y}$

Step 3

Combine

\frac{3}{x^{2}}

$\frac{3}{x^{2}}$ and

y^{\frac{1}{2}}

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

\frac{3 y^{\frac{1}{2}}}{x^{2}} \sqrt[3]{8 x^{4} y}

$\frac{3 y^{\frac{1}{2}}}{x^{2}} \sqrt[3]{8 x^{4} y}$

Step 4

Rewrite

8 x^{4} y

$8 x^{4} y$ as

{(2 x)}^{3} (x y)

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

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Step 4.1

Rewrite

8

$8$ as

2^{3}

$2^{3}$ .

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

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

Step 4.2

Factor out

x^{3}

$x^{3}$ .

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

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

Step 4.3

Rewrite

2^{3} x^{3}

$2^{3} x^{3}$ as

{(2 x)}^{3}

${(2 x)}^{3}$ .

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

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

Step 4.4

Add parentheses.

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

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

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

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

Step 5

Pull terms out from under the radical.

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

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

Step 6

Rewrite using the commutative property of multiplication.

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

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

Step 7

Multiply

2 \frac{3 y^{\frac{1}{2}}}{x^{2}}

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

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Step 7.1

Combine

2

$2$ and

\frac{3 y^{\frac{1}{2}}}{x^{2}}

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

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

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

Step 7.2

Multiply

3

$3$ by

2

$2$ .

\frac{6 y^{\frac{1}{2}}}{x^{2}} (x \sqrt[3]{x y})

$\frac{6 y^{\frac{1}{2}}}{x^{2}} (x \sqrt[3]{x y})$

\frac{6 y^{\frac{1}{2}}}{x^{2}} (x \sqrt[3]{x y})

$\frac{6 y^{\frac{1}{2}}}{x^{2}} (x \sqrt[3]{x y})$

Step 8

Cancel the common factor of

x

$x$ .

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Step 8.1

Factor

x

$x$ out of

x^{2}

$x^{2}$ .

\frac{6 y^{\frac{1}{2}}}{x \cdot x} (x \sqrt[3]{x y})

$\frac{6 y^{\frac{1}{2}}}{x \cdot x} (x \sqrt[3]{x y})$

Step 8.2

Factor

x

$x$ out of

x \sqrt[3]{x y}

$x \sqrt[3]{x y}$ .

\frac{6 y^{\frac{1}{2}}}{x \cdot x} (x (\sqrt[3]{x y}))

$\frac{6 y^{\frac{1}{2}}}{x \cdot x} (x (\sqrt[3]{x y}))$

Step 8.3

Cancel the common factor.

\frac{6 y^{\frac{1}{2}}}{x \cdot x} (x \sqrt[3]{x y})

$\frac{6 y^{\frac{1}{2}}}{x \cdot x} (x \sqrt[3]{x y})$

Step 8.4

Rewrite the expression.

\frac{6 y^{\frac{1}{2}}}{x} \sqrt[3]{x y}

$\frac{6 y^{\frac{1}{2}}}{x} \sqrt[3]{x y}$

\frac{6 y^{\frac{1}{2}}}{x} \sqrt[3]{x y}

$\frac{6 y^{\frac{1}{2}}}{x} \sqrt[3]{x y}$

Step 9

Combine

\frac{6 y^{\frac{1}{2}}}{x}

$\frac{6 y^{\frac{1}{2}}}{x}$ and

\sqrt[3]{x y}

$\sqrt[3]{x y}$ .

\frac{6 y^{\frac{1}{2}} \sqrt[3]{x y}}{x}

$\frac{6 y^{\frac{1}{2}} \sqrt[3]{x y}}{x}$