Algebra Examples

$\sqrt[4]{3 x} - 5 = - 8$

Step 1

Move all terms not containing $\sqrt[4]{3 x}$ to the right side of the equation.

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Step 1.1

Add $5$ to both sides of the equation.

$\sqrt[4]{3 x} = - 8 + 5$

Step 1.2

Add $- 8$ and $5$ .

$\sqrt[4]{3 x} = - 3$

Step 2

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

${\sqrt[4]{3 x}}^{4} = {(- 3)}^{4}$

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 $\sqrt[4]{3 x}$ as ${(3 x)}^{\frac{1}{4}}$ .

${({(3 x)}^{\frac{1}{4}})}^{4} = {(- 3)}^{4}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Simplify ${({(3 x)}^{\frac{1}{4}})}^{4}$ .

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Step 3.2.1.1

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

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Step 3.2.1.1.1

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

${(3 x)}^{\frac{1}{4} \cdot 4} = {(- 3)}^{4}$

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.

${(3 x)}^{\frac{1}{4} \cdot 4} = {(- 3)}^{4}$

Step 3.2.1.1.2.2

Rewrite the expression.

${(3 x)}^{1} = {(- 3)}^{4}$

Step 3.2.1.2

Simplify.

$3 x = {(- 3)}^{4}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Raise $- 3$ to the power of $4$ .

$3 x = 81$

Step 4

Divide each term in $3 x = 81$ by $3$ and simplify.

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Step 4.1

Divide each term in $3 x = 81$ by $3$ .

$\frac{3 x}{3} = \frac{81}{3}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $3$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{81}{3}$

Step 4.2.1.2

Divide $x$ by $1$ .

$x = \frac{81}{3}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $81$ by $3$ .

$x = 27$

Step 5

Exclude the solutions that do not make $\sqrt[4]{3 x} - 5 = - 8$ true.

$No solution$