Solve by Factoring x^(2/9)=2

$x^{\frac{2}{9}} = 2$

Step 1

Subtract $2$ from both sides of the equation.

$x^{\frac{2}{9}} - 2 = 0$

Step 2

Add $2$ to both sides of the equation.

$x^{\frac{2}{9}} = 2$

Step 3

Raise each side of the equation to the power of $\frac{9}{2}$ to eliminate the fractional exponent on the left side.

${(x^{\frac{2}{9}})}^{\frac{9}{2}} = \pm 2^{\frac{9}{2}}$

Step 4

Simplify the left side.

Simplify ${(x^{\frac{2}{9}})}^{\frac{9}{2}}$ .

Multiply the exponents in ${(x^{\frac{2}{9}})}^{\frac{9}{2}}$ .

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

$x^{\frac{2}{9} \cdot \frac{9}{2}} = \pm 2^{\frac{9}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$x^{\frac{2}{9} \cdot \frac{9}{2}} = \pm 2^{\frac{9}{2}}$

Rewrite the expression.

$x^{\frac{1}{9} \cdot 9} = \pm 2^{\frac{9}{2}}$

Cancel the common factor of $9$ .

Cancel the common factor.

$x^{\frac{1}{9} \cdot 9} = \pm 2^{\frac{9}{2}}$

Rewrite the expression.

$x^{1} = \pm 2^{\frac{9}{2}}$

Simplify.

$x = \pm 2^{\frac{9}{2}}$

Step 5

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

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

$x = 2^{\frac{9}{2}}$

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

$x = - 2^{\frac{9}{2}}$

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

$x = 2^{\frac{9}{2}}, - 2^{\frac{9}{2}}$