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

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

Add $3$ to both sides of the equation.

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

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

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

Simplify the exponent.

Simplify the left side.

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

Multiply the exponents in ${({(2 x - 1)}^{\frac{1}{3}})}^{3}$ .

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

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

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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

Simplify the right side.

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

$2 x - 1 = 27$

Solve for $x$ .

Move all terms not containing $x$ to the right side of the equation.

Add $1$ to both sides of the equation.

$2 x = 27 + 1$

Add $27$ and $1$ .

$2 x = 28$

Divide each term in $2 x = 28$ by $2$ and simplify.

Divide each term in $2 x = 28$ by $2$ .

$\frac{2 x}{2} = \frac{28}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{28}{2}$

Divide $x$ by $1$ .

$x = \frac{28}{2}$

Simplify the right side.

Divide $28$ by $2$ .

$x = 14$