Basic Math Examples

$1 = \sqrt[3]{4 w^{2}}$

Step 1

Rewrite the equation as $\sqrt[3]{4 w^{2}} = 1$ .

$\sqrt[3]{4 w^{2}} = 1$

Step 2

To remove the radical on the left side of the equation, cube both sides of the equation.

${\sqrt[3]{4 w^{2}}}^{3} = 1^{3}$

Step 3

Simplify each side of the equation.

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Step 3.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{4 w^{2}}$ as ${(4 w^{2})}^{\frac{1}{3}}$ .

${({(4 w^{2})}^{\frac{1}{3}})}^{3} = 1^{3}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Simplify ${({(4 w^{2})}^{\frac{1}{3}})}^{3}$ .

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Step 3.2.1.1

Multiply the exponents in ${({(4 w^{2})}^{\frac{1}{3}})}^{3}$ .

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Step 3.2.1.1.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

${(4 w^{2})}^{\frac{1}{3} \cdot 3} = 1^{3}$

Step 3.2.1.1.2

Cancel the common factor of $3$ .

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Step 3.2.1.1.2.1

Cancel the common factor.

${(4 w^{2})}^{\frac{1}{3} \cdot 3} = 1^{3}$

Step 3.2.1.1.2.2

Rewrite the expression.

${(4 w^{2})}^{1} = 1^{3}$

Step 3.2.1.2

Simplify.

$4 w^{2} = 1^{3}$

Step 3.3

Simplify the right side.

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Step 3.3.1

One to any power is one.

$4 w^{2} = 1$

Step 4

Solve for $w$ .

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Step 4.1

Divide each term in $4 w^{2} = 1$ by $4$ and simplify.

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Step 4.1.1

Divide each term in $4 w^{2} = 1$ by $4$ .

$\frac{4 w^{2}}{4} = \frac{1}{4}$

Step 4.1.2

Simplify the left side.

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Step 4.1.2.1

Cancel the common factor of $4$ .

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Step 4.1.2.1.1

Cancel the common factor.

$\frac{4 w^{2}}{4} = \frac{1}{4}$

Step 4.1.2.1.2

Divide $w^{2}$ by $1$ .

$w^{2} = \frac{1}{4}$

Step 4.2

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

$w = \pm \sqrt{\frac{1}{4}}$

Step 4.3

Simplify $\pm \sqrt{\frac{1}{4}}$ .

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Step 4.3.1

Rewrite $\sqrt{\frac{1}{4}}$ as $\frac{\sqrt{1}}{\sqrt{4}}$ .

$w = \pm \frac{\sqrt{1}}{\sqrt{4}}$

Step 4.3.2

Any root of $1$ is $1$ .

$w = \pm \frac{1}{\sqrt{4}}$

Step 4.3.3

Simplify the denominator.

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Step 4.3.3.1

Rewrite $4$ as $2^{2}$ .

$w = \pm \frac{1}{\sqrt{2^{2}}}$

Step 4.3.3.2

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

$w = \pm \frac{1}{2}$

Step 4.4

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

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Step 4.4.1

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

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

Step 4.4.2

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

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

Step 4.4.3

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

$w = \frac{1}{2}, - \frac{1}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$w = \frac{1}{2}, - \frac{1}{2}$

Decimal Form:

$w = 0.5, - 0.5$