Algebra Examples

$y = \frac{1}{6} x^{3}$

Step 1

Rewrite the equation as $\frac{1}{6} x^{3} = y$ .

$\frac{1}{6} x^{3} = y$

Step 2

Multiply both sides of the equation by $6$ .

$6 (\frac{1}{6} x^{3}) = 6 y$

Step 3

Simplify the left side.

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Step 3.1

Simplify $6 (\frac{1}{6} x^{3})$ .

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Step 3.1.1

Combine $\frac{1}{6}$ and $x^{3}$ .

$6 \frac{x^{3}}{6} = 6 y$

Step 3.1.2

Cancel the common factor of $6$ .

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Step 3.1.2.1

Cancel the common factor.

$6 \frac{x^{3}}{6} = 6 y$

Step 3.1.2.2

Rewrite the expression.

$x^{3} = 6 y$

Step 4

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$x = \sqrt[3]{6 y}$

Step 5

To rewrite as a function of $y$ , write the equation so that $x$ is by itself on one side of the equal sign and an expression involving only $y$ is on the other side.

$f (y) = \sqrt[3]{6 y}$