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

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

Step 1

Add $2$ to both sides of the equation.

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

Step 2

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

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

Step 3

Simplify the exponent.

Simplify the left side.

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

Apply the product rule to $2 x^{\frac{1}{3}}$ .

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

Raise $2$ to the power of $3$ .

$8 {(x^{\frac{1}{3}})}^{3} = 2^{3}$

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

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

$8 x^{\frac{1}{3} \cdot 3} = 2^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

$8 x^{\frac{1}{3} \cdot 3} = 2^{3}$

Rewrite the expression.

$8 x^{1} = 2^{3}$

Simplify.

$8 x = 2^{3}$

Simplify the right side.

Raise $2$ to the power of $3$ .

$8 x = 8$

Step 4

Divide each term in $8 x = 8$ by $8$ and simplify.

Divide each term in $8 x = 8$ by $8$ .

$\frac{8 x}{8} = \frac{8}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 x}{8} = \frac{8}{8}$

Divide $x$ by $1$ .

$x = \frac{8}{8}$

Simplify the right side.

Divide $8$ by $8$ .

$x = 1$