Solve for p -7+(16p+8)^(1/3)=-1

$- 7 + {(16 p + 8)}^{\frac{1}{3}} = - 1$

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

Add $7$ to both sides of the equation.

${(16 p + 8)}^{\frac{1}{3}} = - 1 + 7$

Add $- 1$ and $7$ .

${(16 p + 8)}^{\frac{1}{3}} = 6$

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

${({(16 p + 8)}^{\frac{1}{3}})}^{3} = 6^{3}$

Simplify the exponent.

Simplify the left side.

Simplify ${({(16 p + 8)}^{\frac{1}{3}})}^{3}$ .

Multiply the exponents in ${({(16 p + 8)}^{\frac{1}{3}})}^{3}$ .

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

${(16 p + 8)}^{\frac{1}{3} \cdot 3} = 6^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

${(16 p + 8)}^{\frac{1}{3} \cdot 3} = 6^{3}$

Rewrite the expression.

${(16 p + 8)}^{1} = 6^{3}$

Simplify.

$16 p + 8 = 6^{3}$

Simplify the right side.

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

$16 p + 8 = 216$

Solve for $p$ .

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

Subtract $8$ from both sides of the equation.

$16 p = 216 - 8$

Subtract $8$ from $216$ .

$16 p = 208$

Divide each term in $16 p = 208$ by $16$ and simplify.

Divide each term in $16 p = 208$ by $16$ .

$\frac{16 p}{16} = \frac{208}{16}$

Simplify the left side.

Cancel the common factor of $16$ .

Cancel the common factor.

$\frac{16 p}{16} = \frac{208}{16}$

Divide $p$ by $1$ .

$p = \frac{208}{16}$

Simplify the right side.

Divide $208$ by $16$ .

$p = 13$