Algebra Examples

$\frac{1}{3} x^{4} = 27$

Step 1

Multiply both sides of the equation by $3$ .

$3 (\frac{1}{3} x^{4}) = 3 \cdot 27$

Step 2

Simplify both sides of the equation.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $3 (\frac{1}{3} x^{4})$ .

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Step 2.1.1.1

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

$3 \frac{x^{4}}{3} = 3 \cdot 27$

Step 2.1.1.2

Cancel the common factor of $3$ .

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Step 2.1.1.2.1

Cancel the common factor.

$3 \frac{x^{4}}{3} = 3 \cdot 27$

Step 2.1.1.2.2

Rewrite the expression.

$x^{4} = 3 \cdot 27$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply $3$ by $27$ .

$x^{4} = 81$

Step 3

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

$x = \pm \sqrt[4]{81}$

Step 4

Simplify $\pm \sqrt[4]{81}$ .

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Step 4.1

Rewrite $81$ as $3^{4}$ .

$x = \pm \sqrt[4]{3^{4}}$

Step 4.2

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

$x = \pm 3$

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.

$x = 3$

Step 5.2

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

$x = - 3$

Step 5.3

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

$x = 3, - 3$