Algebra Examples

$3 \sqrt[3]{2 x} = \sqrt[3]{2 x + 156}$

Step 1

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

${(3 \sqrt[3]{2 x})}^{3} = {\sqrt[3]{2 x + 156}}^{3}$

Step 2

Simplify each side of the equation.

Tap for more steps...

Step 2.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{2 x}$ as ${(2 x)}^{\frac{1}{3}}$ .

${(3 {(2 x)}^{\frac{1}{3}})}^{3} = {\sqrt[3]{2 x + 156}}^{3}$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Simplify ${(3 {(2 x)}^{\frac{1}{3}})}^{3}$ .

Tap for more steps...

Step 2.2.1.1

Apply the product rule to $2 x$ .

${(3 (2^{\frac{1}{3}} x^{\frac{1}{3}}))}^{3} = {\sqrt[3]{2 x + 156}}^{3}$

Step 2.2.1.2

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

Tap for more steps...

Step 2.2.1.2.1

Apply the product rule to $3 \cdot 2^{\frac{1}{3}} x^{\frac{1}{3}}$ .

${(3 \cdot 2^{\frac{1}{3}})}^{3} {(x^{\frac{1}{3}})}^{3} = {\sqrt[3]{2 x + 156}}^{3}$

Step 2.2.1.2.2

Apply the product rule to $3 \cdot 2^{\frac{1}{3}}$ .

$3^{3} \cdot {(2^{\frac{1}{3}})}^{3} {(x^{\frac{1}{3}})}^{3} = {\sqrt[3]{2 x + 156}}^{3}$

Step 2.2.1.3

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

$27 \cdot {(2^{\frac{1}{3}})}^{3} {(x^{\frac{1}{3}})}^{3} = {\sqrt[3]{2 x + 156}}^{3}$

Step 2.2.1.4

Multiply the exponents in ${(2^{\frac{1}{3}})}^{3}$ .

Tap for more steps...

Step 2.2.1.4.1

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

$27 \cdot 2^{\frac{1}{3} \cdot 3} {(x^{\frac{1}{3}})}^{3} = {\sqrt[3]{2 x + 156}}^{3}$

Step 2.2.1.4.2

Cancel the common factor of $3$ .

Tap for more steps...

Step 2.2.1.4.2.1

Cancel the common factor.

$27 \cdot 2^{\frac{1}{3} \cdot 3} {(x^{\frac{1}{3}})}^{3} = {\sqrt[3]{2 x + 156}}^{3}$

Step 2.2.1.4.2.2

Rewrite the expression.

$27 \cdot 2^{1} {(x^{\frac{1}{3}})}^{3} = {\sqrt[3]{2 x + 156}}^{3}$

Step 2.2.1.5

Evaluate the exponent.

$27 \cdot 2 {(x^{\frac{1}{3}})}^{3} = {\sqrt[3]{2 x + 156}}^{3}$

Step 2.2.1.6

Multiply $27$ by $2$ .

$54 {(x^{\frac{1}{3}})}^{3} = {\sqrt[3]{2 x + 156}}^{3}$

Step 2.2.1.7

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

Tap for more steps...

Step 2.2.1.7.1

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

$54 x^{\frac{1}{3} \cdot 3} = {\sqrt[3]{2 x + 156}}^{3}$

Step 2.2.1.7.2

Cancel the common factor of $3$ .

Tap for more steps...

Step 2.2.1.7.2.1

Cancel the common factor.

$54 x^{\frac{1}{3} \cdot 3} = {\sqrt[3]{2 x + 156}}^{3}$

Step 2.2.1.7.2.2

Rewrite the expression.

$54 x^{1} = {\sqrt[3]{2 x + 156}}^{3}$

Step 2.2.1.8

Simplify.

$54 x = {\sqrt[3]{2 x + 156}}^{3}$

Step 2.3

Simplify the right side.

Tap for more steps...

Step 2.3.1

Simplify ${\sqrt[3]{2 x + 156}}^{3}$ .

Tap for more steps...

Step 2.3.1.1

Factor $2$ out of $2 x + 156$ .

Tap for more steps...

Step 2.3.1.1.1

Factor $2$ out of $2 x$ .

$54 x = {\sqrt[3]{2 (x) + 156}}^{3}$

Step 2.3.1.1.2

Factor $2$ out of $156$ .

$54 x = {\sqrt[3]{2 x + 2 \cdot 78}}^{3}$

Step 2.3.1.1.3

Factor $2$ out of $2 x + 2 \cdot 78$ .

$54 x = {\sqrt[3]{2 (x + 78)}}^{3}$

Step 2.3.1.2

Rewrite ${\sqrt[3]{2 (x + 78)}}^{3}$ as $2 (x + 78)$ .

Tap for more steps...

Step 2.3.1.2.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt[3]{2 (x + 78)}$ as ${(2 (x + 78))}^{\frac{1}{3}}$ .

$54 x = {({(2 (x + 78))}^{\frac{1}{3}})}^{3}$

Step 2.3.1.2.2

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

$54 x = {(2 (x + 78))}^{\frac{1}{3} \cdot 3}$

Step 2.3.1.2.3

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

$54 x = {(2 (x + 78))}^{\frac{3}{3}}$

Step 2.3.1.2.4

Cancel the common factor of $3$ .

Tap for more steps...

Step 2.3.1.2.4.1

Cancel the common factor.

$54 x = {(2 (x + 78))}^{\frac{3}{3}}$

Step 2.3.1.2.4.2

Rewrite the expression.

$54 x = {(2 (x + 78))}^{1}$

Step 2.3.1.2.5

Simplify.

$54 x = 2 (x + 78)$

Step 2.3.1.3

Apply the distributive property.

$54 x = 2 x + 2 \cdot 78$

Step 2.3.1.4

Multiply $2$ by $78$ .

$54 x = 2 x + 156$

Step 3

Solve for $x$ .

Tap for more steps...

Step 3.1

Move all terms containing $x$ to the left side of the equation.

Tap for more steps...

Step 3.1.1

Subtract $2 x$ from both sides of the equation.

$54 x - 2 x = 156$

Step 3.1.2

Subtract $2 x$ from $54 x$ .

$52 x = 156$

Step 3.2

Divide each term in $52 x = 156$ by $52$ and simplify.

Tap for more steps...

Step 3.2.1

Divide each term in $52 x = 156$ by $52$ .

$\frac{52 x}{52} = \frac{156}{52}$

Step 3.2.2

Simplify the left side.

Tap for more steps...

Step 3.2.2.1

Cancel the common factor of $52$ .

Tap for more steps...

Step 3.2.2.1.1

Cancel the common factor.

$\frac{52 x}{52} = \frac{156}{52}$

Step 3.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{156}{52}$

Step 3.2.3

Simplify the right side.

Tap for more steps...

Step 3.2.3.1

Divide $156$ by $52$ .

$x = 3$