Algebra Examples

$\frac{1}{5} \sqrt[3]{3 x} + 10 = 8$

Step 1

Move all terms not containing $\frac{1}{5} \cdot \sqrt[3]{3 x}$ to the right side of the equation.

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Step 1.1

Subtract $10$ from both sides of the equation.

$\frac{1}{5} \cdot \sqrt[3]{3 x} = 8 - 10$

Step 1.2

Subtract $10$ from $8$ .

$\frac{1}{5} \cdot \sqrt[3]{3 x} = - 2$

Step 2

To remove the radical on the left side of the equation, cube both sides of the equation.

${(\frac{1}{5} \cdot \sqrt[3]{3 x})}^{3} = {(- 2)}^{3}$

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

${(\frac{1}{5} \cdot {(3 x)}^{\frac{1}{3}})}^{3} = {(- 2)}^{3}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Simplify ${(\frac{1}{5} \cdot {(3 x)}^{\frac{1}{3}})}^{3}$ .

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Step 3.2.1.1

Apply the product rule to $3 x$ .

${(\frac{1}{5} \cdot (3^{\frac{1}{3}} x^{\frac{1}{3}}))}^{3} = {(- 2)}^{3}$

Step 3.2.1.2

Multiply $\frac{1}{5} (3^{\frac{1}{3}} x^{\frac{1}{3}})$ .

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Step 3.2.1.2.1

Combine $3^{\frac{1}{3}}$ and $\frac{1}{5}$ .

${(\frac{3^{\frac{1}{3}}}{5} x^{\frac{1}{3}})}^{3} = {(- 2)}^{3}$

Step 3.2.1.2.2

Combine $\frac{3^{\frac{1}{3}}}{5}$ and $x^{\frac{1}{3}}$ .

${(\frac{3^{\frac{1}{3}} x^{\frac{1}{3}}}{5})}^{3} = {(- 2)}^{3}$

Step 3.2.1.3

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 3.2.1.3.1

Apply the product rule to $\frac{3^{\frac{1}{3}} x^{\frac{1}{3}}}{5}$ .

$\frac{{(3^{\frac{1}{3}} x^{\frac{1}{3}})}^{3}}{5^{3}} = {(- 2)}^{3}$

Step 3.2.1.3.2

Apply the product rule to $3^{\frac{1}{3}} x^{\frac{1}{3}}$ .

$\frac{{(3^{\frac{1}{3}})}^{3} {(x^{\frac{1}{3}})}^{3}}{5^{3}} = {(- 2)}^{3}$

Step 3.2.1.4

Simplify the numerator.

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Step 3.2.1.4.1

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

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Step 3.2.1.4.1.1

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

$\frac{3^{\frac{1}{3} \cdot 3} {(x^{\frac{1}{3}})}^{3}}{5^{3}} = {(- 2)}^{3}$

Step 3.2.1.4.1.2

Cancel the common factor of $3$ .

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Step 3.2.1.4.1.2.1

Cancel the common factor.

$\frac{3^{\frac{1}{3} \cdot 3} {(x^{\frac{1}{3}})}^{3}}{5^{3}} = {(- 2)}^{3}$

Step 3.2.1.4.1.2.2

Rewrite the expression.

$\frac{3^{1} {(x^{\frac{1}{3}})}^{3}}{5^{3}} = {(- 2)}^{3}$

Step 3.2.1.4.2

Evaluate the exponent.

$\frac{3 {(x^{\frac{1}{3}})}^{3}}{5^{3}} = {(- 2)}^{3}$

Step 3.2.1.4.3

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

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Step 3.2.1.4.3.1

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

$\frac{3 x^{\frac{1}{3} \cdot 3}}{5^{3}} = {(- 2)}^{3}$

Step 3.2.1.4.3.2

Cancel the common factor of $3$ .

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Step 3.2.1.4.3.2.1

Cancel the common factor.

$\frac{3 x^{\frac{1}{3} \cdot 3}}{5^{3}} = {(- 2)}^{3}$

Step 3.2.1.4.3.2.2

Rewrite the expression.

$\frac{3 x^{1}}{5^{3}} = {(- 2)}^{3}$

Step 3.2.1.4.4

Simplify.

$\frac{3 x}{5^{3}} = {(- 2)}^{3}$

Step 3.2.1.5

Raise $5$ to the power of $3$ .

$\frac{3 x}{125} = {(- 2)}^{3}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Raise $- 2$ to the power of $3$ .

$\frac{3 x}{125} = - 8$

Step 4

Solve for $x$ .

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Step 4.1

Multiply both sides of the equation by $\frac{125}{3}$ .

$\frac{125}{3} \cdot \frac{3 x}{125} = \frac{125}{3} \cdot - 8$

Step 4.2

Simplify both sides of the equation.

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Step 4.2.1

Simplify the left side.

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Step 4.2.1.1

Simplify $\frac{125}{3} \cdot \frac{3 x}{125}$ .

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Step 4.2.1.1.1

Cancel the common factor of $125$ .

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Step 4.2.1.1.1.1

Cancel the common factor.

$\frac{125}{3} \cdot \frac{3 x}{125} = \frac{125}{3} \cdot - 8$

Step 4.2.1.1.1.2

Rewrite the expression.

$\frac{1}{3} (3 x) = \frac{125}{3} \cdot - 8$

Step 4.2.1.1.2

Cancel the common factor of $3$ .

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Step 4.2.1.1.2.1

Factor $3$ out of $3 x$ .

$\frac{1}{3} (3 (x)) = \frac{125}{3} \cdot - 8$

Step 4.2.1.1.2.2

Cancel the common factor.

$\frac{1}{3} (3 x) = \frac{125}{3} \cdot - 8$

Step 4.2.1.1.2.3

Rewrite the expression.

$x = \frac{125}{3} \cdot - 8$

Step 4.2.2

Simplify the right side.

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Step 4.2.2.1

Simplify $\frac{125}{3} \cdot - 8$ .

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Step 4.2.2.1.1

Multiply $\frac{125}{3} \cdot - 8$ .

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Step 4.2.2.1.1.1

Combine $\frac{125}{3}$ and $- 8$ .

$x = \frac{125 \cdot - 8}{3}$

Step 4.2.2.1.1.2

Multiply $125$ by $- 8$ .

$x = \frac{- 1000}{3}$

Step 4.2.2.1.2

Move the negative in front of the fraction.

$x = - \frac{1000}{3}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{1000}{3}$

Decimal Form:

$x = - 333.\overline{3}$

Mixed Number Form:

$x = - 333 \frac{1}{3}$