Solve for X X^(2/3)=0

$X^{\frac{2}{3}} = 0$

Step 1

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

${(X^{\frac{2}{3}})}^{\frac{3}{2}} = \pm 0^{\frac{3}{2}}$

Step 2

Simplify the exponent.

Simplify the left side.

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

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

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

$X^{\frac{2}{3} \cdot \frac{3}{2}} = \pm 0^{\frac{3}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$X^{\frac{2}{3} \cdot \frac{3}{2}} = \pm 0^{\frac{3}{2}}$

Rewrite the expression.

$X^{\frac{1}{3} \cdot 3} = \pm 0^{\frac{3}{2}}$

Cancel the common factor of $3$ .

Cancel the common factor.

$X^{\frac{1}{3} \cdot 3} = \pm 0^{\frac{3}{2}}$

Rewrite the expression.

$X^{1} = \pm 0^{\frac{3}{2}}$

Simplify.

$X = \pm 0^{\frac{3}{2}}$

Simplify the right side.

Simplify $\pm 0^{\frac{3}{2}}$ .

Simplify the expression.

Rewrite $0$ as $0^{2}$ .

$X = \pm {(0^{2})}^{\frac{3}{2}}$

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

$X = \pm 0^{2 (\frac{3}{2})}$

Cancel the common factor of $2$ .

Cancel the common factor.

$X = \pm 0^{2 (\frac{3}{2})}$

Rewrite the expression.

$X = \pm 0^{3}$

Raising $0$ to any positive power yields $0$ .

$X = \pm 0$

Plus or minus $0$ is $0$ .

$X = 0$