Solve by Factoring 2x^(1/3)-2=0

$2 x^{\frac{1}{3}} - 2 = 0$

Step 1

Factor $2$ out of $2 x^{\frac{1}{3}} - 2$ .

Factor $2$ out of $2 x^{\frac{1}{3}}$ .

$2 (x^{\frac{1}{3}}) - 2 = 0$

Factor $2$ out of $- 2$ .

$2 (x^{\frac{1}{3}}) + 2 (- 1) = 0$

Factor $2$ out of $2 (x^{\frac{1}{3}}) + 2 (- 1)$ .

$2 (x^{\frac{1}{3}} - 1) = 0$

Step 2

Divide each term in $2 (x^{\frac{1}{3}} - 1) = 0$ by $2$ and simplify.

Divide each term in $2 (x^{\frac{1}{3}} - 1) = 0$ by $2$ .

$\frac{2 (x^{\frac{1}{3}} - 1)}{2} = \frac{0}{2}$

Simplify the left side.

Cancel the common factor.

$\frac{2 (x^{\frac{1}{3}} - 1)}{2} = \frac{0}{2}$

Divide $x^{\frac{1}{3}} - 1$ by $1$ .

$x^{\frac{1}{3}} - 1 = \frac{0}{2}$

Simplify the right side.

Divide $0$ by $2$ .

$x^{\frac{1}{3}} - 1 = 0$

Step 3

Add $1$ to both sides of the equation.

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

Step 4

Raise each side of the equation to the power of $3$ to eliminate the fractional exponent on the left side.

${(x^{\frac{1}{3}})}^{3} = 1^{3}$

Step 5

Simplify the exponent.

Simplify the left side.

Simplify ${(x^{\frac{1}{3}})}^{3}$ .

Multiply the exponents in ${(x^{\frac{1}{3}})}^{3}$ .

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

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

$x^{1} = 1^{3}$

Simplify.

$x = 1^{3}$

Simplify the right side.

One to any power is one.

$x = 1$