Algebra Examples

$\sqrt[5]{8 x + 16} + 1 = - 1$

Step 1

Move all terms not containing $\sqrt[5]{8 x + 16}$ to the right side of the equation.

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Step 1.1

Subtract $1$ from both sides of the equation.

$\sqrt[5]{8 x + 16} = - 1 - 1$

Step 1.2

Subtract $1$ from $- 1$ .

$\sqrt[5]{8 x + 16} = - 2$

Step 2

To remove the radical on the left side of the equation, raise both sides of the equation to the power of $5$ .

${\sqrt[5]{8 x + 16}}^{5} = {(- 2)}^{5}$

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 $\sqrt[5]{8 x + 16}$ as ${(8 x + 16)}^{\frac{1}{5}}$ .

${({(8 x + 16)}^{\frac{1}{5}})}^{5} = {(- 2)}^{5}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Simplify ${({(8 x + 16)}^{\frac{1}{5}})}^{5}$ .

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Step 3.2.1.1

Multiply the exponents in ${({(8 x + 16)}^{\frac{1}{5}})}^{5}$ .

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Step 3.2.1.1.1

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

${(8 x + 16)}^{\frac{1}{5} \cdot 5} = {(- 2)}^{5}$

Step 3.2.1.1.2

Cancel the common factor of $5$ .

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Step 3.2.1.1.2.1

Cancel the common factor.

${(8 x + 16)}^{\frac{1}{5} \cdot 5} = {(- 2)}^{5}$

Step 3.2.1.1.2.2

Rewrite the expression.

${(8 x + 16)}^{1} = {(- 2)}^{5}$

Step 3.2.1.2

Simplify.

$8 x + 16 = {(- 2)}^{5}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Raise $- 2$ to the power of $5$ .

$8 x + 16 = - 32$

Step 4

Solve for $x$ .

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Step 4.1

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

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Step 4.1.1

Subtract $16$ from both sides of the equation.

$8 x = - 32 - 16$

Step 4.1.2

Subtract $16$ from $- 32$ .

$8 x = - 48$

Step 4.2

Divide each term in $8 x = - 48$ by $8$ and simplify.

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Step 4.2.1

Divide each term in $8 x = - 48$ by $8$ .

$\frac{8 x}{8} = \frac{- 48}{8}$

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.

$\frac{8 x}{8} = \frac{- 48}{8}$

Step 4.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 48}{8}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Divide $- 48$ by $8$ .

$x = - 6$