Algebra Examples

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

Step 1

Substitute $- 2$ for $x$ and find the result for $y$ .

$y = \frac{1}{2} \cdot \sqrt[3]{- 2}$

Step 2

Simplify $\frac{1}{2} \cdot \sqrt[3]{- 2}$ .

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Step 2.1

Remove parentheses.

$y = \frac{1}{2} \cdot \sqrt[3]{- 2}$

Step 2.2

Rewrite $- 2$ as ${(- 1)}^{3} \cdot 2$ .

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Step 2.2.1

Rewrite $- 2$ as $- 1 (2)$ .

$y = \frac{1}{2} \cdot \sqrt[3]{- 1 (2)}$

Step 2.2.2

Rewrite $- 1$ as ${(- 1)}^{3}$ .

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

Step 2.3

Pull terms out from under the radical.

$y = \frac{1}{2} \cdot (- 1 \sqrt[3]{2})$

Step 2.4

Rewrite $- 1 \sqrt[3]{2}$ as $- \sqrt[3]{2}$ .

$y = \frac{1}{2} \cdot (- \sqrt[3]{2})$

Step 2.5

Combine $\frac{1}{2}$ and $\sqrt[3]{2}$ .

$y = - \frac{\sqrt[3]{2}}{2}$

Step 3

Substitute $- 1$ for $x$ and find the result for $y$ .

$y = \frac{1}{2} \cdot \sqrt[3]{- 1}$

Step 4

Simplify $\frac{1}{2} \cdot \sqrt[3]{- 1}$ .

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Step 4.1

Remove parentheses.

$y = \frac{1}{2} \cdot \sqrt[3]{- 1}$

Step 4.2

Rewrite $- 1$ as ${(- 1)}^{3}$ .

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

Step 4.3

Pull terms out from under the radical, assuming real numbers.

$y = \frac{1}{2} \cdot - 1$

Step 4.4

Combine $\frac{1}{2}$ and $- 1$ .

$y = \frac{- 1}{2}$

Step 4.5

Move the negative in front of the fraction.

$y = - \frac{1}{2}$

Step 5

Substitute $0$ for $x$ and find the result for $y$ .

$y = \frac{1}{2} \cdot \sqrt[3]{0}$

Step 6

Simplify $\frac{1}{2} \cdot \sqrt[3]{0}$ .

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Step 6.1

Remove parentheses.

$y = \frac{1}{2} \cdot \sqrt[3]{0}$

Step 6.2

Rewrite $0$ as $0^{3}$ .

$y = \frac{1}{2} \cdot \sqrt[3]{0^{3}}$

Step 6.3

Pull terms out from under the radical, assuming real numbers.

$y = \frac{1}{2} \cdot 0$

Step 6.4

Multiply $\frac{1}{2}$ by $0$ .

$y = 0$

Step 7

Substitute $1$ for $x$ and find the result for $y$ .

$y = \frac{1}{2} \cdot \sqrt[3]{1}$

Step 8

Simplify $\frac{1}{2} \cdot \sqrt[3]{1}$ .

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Step 8.1

Remove parentheses.

$y = \frac{1}{2} \cdot \sqrt[3]{1}$

Step 8.2

Any root of $1$ is $1$ .

$y = \frac{1}{2} \cdot 1$

Step 8.3

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

$y = \frac{1}{2}$

Step 9

Substitute $2$ for $x$ and find the result for $y$ .

$y = \frac{1}{2} \cdot \sqrt[3]{2}$

Step 10

Simplify $\frac{1}{2} \cdot \sqrt[3]{2}$ .

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Step 10.1

Remove parentheses.

$y = \frac{1}{2} \cdot \sqrt[3]{2}$

Step 10.2

Combine $\frac{1}{2}$ and $\sqrt[3]{2}$ .

$y = \frac{\sqrt[3]{2}}{2}$

Step 11

This is a table of possible values to use when graphing the equation.

$\begin{array}{c} x & y \\ - 2 & - \frac{\sqrt[3]{2}}{2} \\ - 1 & - \frac{1}{2} \\ 0 & 0 \\ 1 & \frac{1}{2} \\ 2 & \frac{\sqrt[3]{2}}{2} \end{array}$

Step 12