Solve for x 3(3x-1)^(1/3)-6=0

$3 {(3 x - 1)}^{\frac{1}{3}} - 6 = 0$

Step 1

Add $6$ to both sides of the equation.

$3 {(3 x - 1)}^{\frac{1}{3}} = 6$

Step 2

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

${(3 {(3 x - 1)}^{\frac{1}{3}})}^{3} = 6^{3}$

Step 3

Simplify the exponent.

Simplify the left side.

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

Apply the product rule to $3 {(3 x - 1)}^{\frac{1}{3}}$ .

$3^{3} {({(3 x - 1)}^{\frac{1}{3}})}^{3} = 6^{3}$

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

$27 {({(3 x - 1)}^{\frac{1}{3}})}^{3} = 6^{3}$

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

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

$27 {(3 x - 1)}^{\frac{1}{3} \cdot 3} = 6^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

$27 {(3 x - 1)}^{\frac{1}{3} \cdot 3} = 6^{3}$

Rewrite the expression.

$27 {(3 x - 1)}^{1} = 6^{3}$

Simplify.

$27 (3 x - 1) = 6^{3}$

Apply the distributive property.

$27 (3 x) + 27 \cdot - 1 = 6^{3}$

Multiply.

Multiply $3$ by $27$ .

$81 x + 27 \cdot - 1 = 6^{3}$

Multiply $27$ by $- 1$ .

$81 x - 27 = 6^{3}$

Simplify the right side.

Raise $6$ to the power of $3$ .

$81 x - 27 = 216$

Step 4

Solve for $x$ .

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

Add $27$ to both sides of the equation.

$81 x = 216 + 27$

Add $216$ and $27$ .

$81 x = 243$

Divide each term in $81 x = 243$ by $81$ and simplify.

Divide each term in $81 x = 243$ by $81$ .

$\frac{81 x}{81} = \frac{243}{81}$

Simplify the left side.

Cancel the common factor of $81$ .

Cancel the common factor.

$\frac{81 x}{81} = \frac{243}{81}$

Divide $x$ by $1$ .

$x = \frac{243}{81}$

Simplify the right side.

Divide $243$ by $81$ .

$x = 3$

Solve for x 3(3x-1)^(1/3)-6=0

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