Solve for v (4v-16)^(1/3)+2=0

${(4 v - 16)}^{\frac{1}{3}} + 2 = 0$

Subtract $2$ from both sides of the equation.

${(4 v - 16)}^{\frac{1}{3}} = - 2$

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

${({(4 v - 16)}^{\frac{1}{3}})}^{3} = {(- 2)}^{3}$

Simplify the exponent.

Simplify the left side.

Simplify ${({(4 v - 16)}^{\frac{1}{3}})}^{3}$ .

Multiply the exponents in ${({(4 v - 16)}^{\frac{1}{3}})}^{3}$ .

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

${(4 v - 16)}^{\frac{1}{3} \cdot 3} = {(- 2)}^{3}$

Cancel the common factor of $3$ .

Cancel the common factor.

${(4 v - 16)}^{\frac{1}{3} \cdot 3} = {(- 2)}^{3}$

Rewrite the expression.

${(4 v - 16)}^{1} = {(- 2)}^{3}$

Simplify.

$4 v - 16 = {(- 2)}^{3}$

Simplify the right side.

Raise $- 2$ to the power of $3$ .

$4 v - 16 = - 8$

Solve for $v$ .

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

Add $16$ to both sides of the equation.

$4 v = - 8 + 16$

Add $- 8$ and $16$ .

$4 v = 8$

Divide each term in $4 v = 8$ by $4$ and simplify.

Divide each term in $4 v = 8$ by $4$ .

$\frac{4 v}{4} = \frac{8}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 v}{4} = \frac{8}{4}$

Divide $v$ by $1$ .

$v = \frac{8}{4}$

Simplify the right side.

Divide $8$ by $4$ .

$v = 2$