Algebra Examples

$x = 6 y^{6}$

Step 1

Rewrite the equation as $6 y^{6} = x$ .

$6 y^{6} = x$

Step 2

Divide each term in $6 y^{6} = x$ by $6$ and simplify.

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Step 2.1

Divide each term in $6 y^{6} = x$ by $6$ .

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

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $6$ .

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Step 2.2.1.1

Cancel the common factor.

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

Step 2.2.1.2

Divide $y^{6}$ by $1$ .

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

Step 3

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

$y = \pm \sqrt[6]{\frac{x}{6}}$

Step 4

Rewrite $\sqrt[6]{\frac{x}{6}}$ as $\frac{\sqrt[6]{x}}{\sqrt[6]{6}}$ .

$y = \pm \frac{\sqrt[6]{x}}{\sqrt[6]{6}}$

Step 5

The complete solution is the result of both the positive and negative portions of the solution.

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Step 5.1

First, use the positive value of the $\pm$ to find the first solution.

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

Step 5.2

Next, use the negative value of the $\pm$ to find the second solution.

$y = - \frac{\sqrt[6]{x}}{\sqrt[6]{6}}$

Step 5.3

The complete solution is the result of both the positive and negative portions of the solution.

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

$y = - \frac{\sqrt[6]{x}}{\sqrt[6]{6}}$

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

$y = - \frac{\sqrt[6]{x}}{\sqrt[6]{6}}$

Step 6

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

$f (x) = \frac{\sqrt[6]{x}}{\sqrt[6]{6}}, - \frac{\sqrt[6]{x}}{\sqrt[6]{6}}$