Algebra Examples

$x^{\frac{2}{3}} = 2$

Step 1

Subtract $2$ from both sides of the equation.

$x^{\frac{2}{3}} - 2 = 0$

Step 2

Add $2$ to both sides of the equation.

$x^{\frac{2}{3}} = 2$

Step 3

Raise each side of the equation to the power of $\frac{3}{2}$ to eliminate the fractional exponent on the left side.

${(x^{\frac{2}{3}})}^{\frac{3}{2}} = \pm 2^{\frac{3}{2}}$

Step 4

Simplify the left side.

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Step 4.1

Simplify ${(x^{\frac{2}{3}})}^{\frac{3}{2}}$ .

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Step 4.1.1

Multiply the exponents in ${(x^{\frac{2}{3}})}^{\frac{3}{2}}$ .

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Step 4.1.1.1

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

$x^{\frac{2}{3} \cdot \frac{3}{2}} = \pm 2^{\frac{3}{2}}$

Step 4.1.1.2

Cancel the common factor of $2$ .

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Step 4.1.1.2.1

Cancel the common factor.

$x^{\frac{2}{3} \cdot \frac{3}{2}} = \pm 2^{\frac{3}{2}}$

Step 4.1.1.2.2

Rewrite the expression.

$x^{\frac{1}{3} \cdot 3} = \pm 2^{\frac{3}{2}}$

Step 4.1.1.3

Cancel the common factor of $3$ .

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Step 4.1.1.3.1

Cancel the common factor.

$x^{\frac{1}{3} \cdot 3} = \pm 2^{\frac{3}{2}}$

Step 4.1.1.3.2

Rewrite the expression.

$x^{1} = \pm 2^{\frac{3}{2}}$

Step 4.1.2

Simplify.

$x = \pm 2^{\frac{3}{2}}$

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.

$x = 2^{\frac{3}{2}}$

Step 5.2

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

$x = - 2^{\frac{3}{2}}$

Step 5.3

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

$x = 2^{\frac{3}{2}}, - 2^{\frac{3}{2}}$