Solve for p (7p-1)^(1/3)+11=7

${(7 p - 1)}^{\frac{1}{3}} + 11 = 7$

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

Subtract $11$ from both sides of the equation.

${(7 p - 1)}^{\frac{1}{3}} = 7 - 11$

Subtract $11$ from $7$ .

${(7 p - 1)}^{\frac{1}{3}} = - 4$

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

${({(7 p - 1)}^{\frac{1}{3}})}^{3} = {(- 4)}^{3}$

Simplify the exponent.

Simplify the left side.

Simplify ${({(7 p - 1)}^{\frac{1}{3}})}^{3}$ .

Multiply the exponents in ${({(7 p - 1)}^{\frac{1}{3}})}^{3}$ .

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

${(7 p - 1)}^{\frac{1}{3} \cdot 3} = {(- 4)}^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

${(7 p - 1)}^{\frac{1}{3} \cdot 3} = {(- 4)}^{3}$

Rewrite the expression.

${(7 p - 1)}^{1} = {(- 4)}^{3}$

Simplify.

$7 p - 1 = {(- 4)}^{3}$

Simplify the right side.

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

$7 p - 1 = - 64$

Solve for $p$ .

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

Add $1$ to both sides of the equation.

$7 p = - 64 + 1$

Add $- 64$ and $1$ .

$7 p = - 63$

Divide each term in $7 p = - 63$ by $7$ and simplify.

Divide each term in $7 p = - 63$ by $7$ .

$\frac{7 p}{7} = \frac{- 63}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 p}{7} = \frac{- 63}{7}$

Divide $p$ by $1$ .

$p = \frac{- 63}{7}$

Simplify the right side.

Divide $- 63$ by $7$ .

$p = - 9$