Algebra Examples

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

Step 1

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

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Step 1.1

Add $9$ to both sides of the equation.

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

Step 1.2

Add $- 11$ and $9$ .

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

Step 2

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

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

Step 3

Simplify each side of the equation.

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Step 3.1

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

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

Step 3.2

Simplify the left side.

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Step 3.2.1

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

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Step 3.2.1.1

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

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Step 3.2.1.1.1

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

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

Step 3.2.1.1.2

Cancel the common factor of $4$ .

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Step 3.2.1.1.2.1

Cancel the common factor.

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

Step 3.2.1.1.2.2

Rewrite the expression.

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

Step 3.2.1.2

Simplify.

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

Step 3.3

Simplify the right side.

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Step 3.3.1

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

$8 k + 12 = 16$

Step 4

Solve for $k$ .

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Step 4.1

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

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Step 4.1.1

Subtract $12$ from both sides of the equation.

$8 k = 16 - 12$

Step 4.1.2

Subtract $12$ from $16$ .

$8 k = 4$

Step 4.2

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

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Step 4.2.1

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

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

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $8$ .

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Step 4.2.2.1.1

Cancel the common factor.

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

Step 4.2.2.1.2

Divide $k$ by $1$ .

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

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

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

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Step 4.2.3.1.1

Factor $4$ out of $4$ .

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

Step 4.2.3.1.2

Cancel the common factors.

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Step 4.2.3.1.2.1

Factor $4$ out of $8$ .

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

Step 4.2.3.1.2.2

Cancel the common factor.

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

Step 4.2.3.1.2.3

Rewrite the expression.

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

Step 5

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

$No solution$