Solve the Rational Equation for x (3x-1)^(1/5)=2

${(3 x - 1)}^{\frac{1}{5}} = 2$

Raise each side of the equation to the power of $5$ to eliminate the fractional exponent on the left side.

${({(3 x - 1)}^{\frac{1}{5}})}^{5} = 2^{5}$

Simplify the exponent.

Simplify the left side.

Simplify ${({(3 x - 1)}^{\frac{1}{5}})}^{5}$ .

Multiply the exponents in ${({(3 x - 1)}^{\frac{1}{5}})}^{5}$ .

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

${(3 x - 1)}^{\frac{1}{5} \cdot 5} = 2^{5}$

Cancel the common factor of $5$ .

Cancel the common factor.

${(3 x - 1)}^{\frac{1}{5} \cdot 5} = 2^{5}$

Rewrite the expression.

${(3 x - 1)}^{1} = 2^{5}$

Simplify.

$3 x - 1 = 2^{5}$

Simplify the right side.

Raise $2$ to the power of $5$ .

$3 x - 1 = 32$

Solve for $x$ .

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

Add $1$ to both sides of the equation.

$3 x = 32 + 1$

Add $32$ and $1$ .

$3 x = 33$

Divide each term in $3 x = 33$ by $3$ and simplify.

Divide each term in $3 x = 33$ by $3$ .

$\frac{3 x}{3} = \frac{33}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{33}{3}$

Divide $x$ by $1$ .

$x = \frac{33}{3}$

Simplify the right side.

Divide $33$ by $3$ .

$x = 11$