Solve the Rational Equation for k fourth root of 8k+12-9=-11

$\sqrt[4]{8 k + 12} - 9 = - 11$

Move all terms not containing $\sqrt[4]{8 k + 12}$ to the right side of the equation.

Add $9$ to both sides of the equation.

$\sqrt[4]{8 k + 12} = - 11 + 9$

Add $- 11$ and $9$ .

$\sqrt[4]{8 k + 12} = - 2$

To remove the radical on the left side of the equation, raise both sides of the equation to the power of $4$ .

${\sqrt[4]{8 k + 12}}^{4} = {(- 2)}^{4}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[4]{8 k + 12}$ as ${(8 k + 12)}^{\frac{1}{4}}$ .

${({(8 k + 12)}^{\frac{1}{4}})}^{4} = {(- 2)}^{4}$

Simplify the left side.

Simplify ${({(8 k + 12)}^{\frac{1}{4}})}^{4}$ .

Multiply the exponents in ${({(8 k + 12)}^{\frac{1}{4}})}^{4}$ .

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

${(8 k + 12)}^{\frac{1}{4} \cdot 4} = {(- 2)}^{4}$

Cancel the common factor of $4$ .

Cancel the common factor.

${(8 k + 12)}^{\frac{1}{4} \cdot 4} = {(- 2)}^{4}$

Rewrite the expression.

${(8 k + 12)}^{1} = {(- 2)}^{4}$

Simplify.

$8 k + 12 = {(- 2)}^{4}$

Simplify the right side.

Raise $- 2$ to the power of $4$ .

$8 k + 12 = 16$

Solve for $k$ .

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

Subtract $12$ from both sides of the equation.

$8 k = 16 - 12$

Subtract $12$ from $16$ .

$8 k = 4$

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

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

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

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

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

Divide $k$ by $1$ .

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

Simplify the right side.

Cancel the common factor of $4$ and $8$ .

Factor $4$ out of $4$ .

$k = \frac{4 (1)}{8}$

Cancel the common factors.

Factor $4$ out of $8$ .

$k = \frac{4 \cdot 1}{4 \cdot 2}$

Cancel the common factor.

$k = \frac{4 \cdot 1}{4 \cdot 2}$

Rewrite the expression.

$k = \frac{1}{2}$

Exclude the solutions that do not make $\sqrt[4]{8 k + 12} - 9 = - 11$ true.

$No solution$

Solve the Rational Equation for k fourth root of 8k+12-9=-11

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