Solve for v (7v-2)^(1/4)+12=7

${(7 v - 2)}^{\frac{1}{4}} + 12 = 7$

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

Subtract $12$ from both sides of the equation.

${(7 v - 2)}^{\frac{1}{4}} = 7 - 12$

Subtract $12$ from $7$ .

${(7 v - 2)}^{\frac{1}{4}} = - 5$

Raise each side of the equation to the power of $4$ to eliminate the fractional exponent on the left side.

${({(7 v - 2)}^{\frac{1}{4}})}^{4} = {(- 5)}^{4}$

Simplify the exponent.

Simplify the left side.

Simplify ${({(7 v - 2)}^{\frac{1}{4}})}^{4}$ .

Multiply the exponents in ${({(7 v - 2)}^{\frac{1}{4}})}^{4}$ .

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

${(7 v - 2)}^{\frac{1}{4} \cdot 4} = {(- 5)}^{4}$

Cancel the common factor of $4$ .

Cancel the common factor.

${(7 v - 2)}^{\frac{1}{4} \cdot 4} = {(- 5)}^{4}$

Rewrite the expression.

${(7 v - 2)}^{1} = {(- 5)}^{4}$

Simplify.

$7 v - 2 = {(- 5)}^{4}$

Simplify the right side.

Raise $- 5$ to the power of $4$ .

$7 v - 2 = 625$

Solve for $v$ .

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

Add $2$ to both sides of the equation.

$7 v = 625 + 2$

Add $625$ and $2$ .

$7 v = 627$

Divide each term in $7 v = 627$ by $7$ and simplify.

Divide each term in $7 v = 627$ by $7$ .

$\frac{7 v}{7} = \frac{627}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 v}{7} = \frac{627}{7}$

Divide $v$ by $1$ .

$v = \frac{627}{7}$

Exclude the solutions that do not make ${(7 v - 2)}^{\frac{1}{4}} + 12 = 7$ true.

$No solution$