Algebra Examples

$\frac{1}{2} x^{5} = 512$

Step 1

Multiply both sides of the equation by $2$ .

$2 (\frac{1}{2} x^{5}) = 2 \cdot 512$

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 $2 (\frac{1}{2} x^{5})$ .

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Step 2.1.1.1

Combine $\frac{1}{2}$ and $x^{5}$ .

$2 \frac{x^{5}}{2} = 2 \cdot 512$

Step 2.1.1.2

Cancel the common factor of $2$ .

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Step 2.1.1.2.1

Cancel the common factor.

$2 \frac{x^{5}}{2} = 2 \cdot 512$

Step 2.1.1.2.2

Rewrite the expression.

$x^{5} = 2 \cdot 512$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply $2$ by $512$ .

$x^{5} = 1024$

Step 3

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

$x = \sqrt[5]{1024}$

Step 4

Simplify $\sqrt[5]{1024}$ .

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Step 4.1

Rewrite $1024$ as $4^{5}$ .

$x = \sqrt[5]{4^{5}}$

Step 4.2

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

$x = 4$