Solve for z (5z-1)^(1/3)-3=1

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

Step 1

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

Add $3$ to both sides of the equation.

${(5 z - 1)}^{\frac{1}{3}} = 1 + 3$

Add $1$ and $3$ .

${(5 z - 1)}^{\frac{1}{3}} = 4$

Step 2

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

${({(5 z - 1)}^{\frac{1}{3}})}^{3} = 4^{3}$

Step 3

Simplify the exponent.

Simplify the left side.

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

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

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

${(5 z - 1)}^{\frac{1}{3} \cdot 3} = 4^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

${(5 z - 1)}^{\frac{1}{3} \cdot 3} = 4^{3}$

Rewrite the expression.

${(5 z - 1)}^{1} = 4^{3}$

Simplify.

$5 z - 1 = 4^{3}$

Simplify the right side.

Raise $4$ to the power of $3$ .

$5 z - 1 = 64$

Step 4

Solve for $z$ .

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

Add $1$ to both sides of the equation.

$5 z = 64 + 1$

Add $64$ and $1$ .

$5 z = 65$

Divide each term in $5 z = 65$ by $5$ and simplify.

Divide each term in $5 z = 65$ by $5$ .

$\frac{5 z}{5} = \frac{65}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 z}{5} = \frac{65}{5}$

Divide $z$ by $1$ .

$z = \frac{65}{5}$

Simplify the right side.

Divide $65$ by $5$ .

$z = 13$

Solve for z (5z-1)^(1/3)-3=1

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