Algebra Examples

$6 x^{\frac{2}{3}} = 2 x$

Step 1

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

$6 x^{\frac{2}{3}} - 2 x = 0$

Step 2

Factor $2 x^{\frac{2}{3}}$ out of $6 x^{\frac{2}{3}} - 2 x$ .

Tap for more steps...

Step 2.1

Factor $2 x^{\frac{2}{3}}$ out of $6 x^{\frac{2}{3}}$ .

$2 x^{\frac{2}{3}} (3) - 2 x = 0$

Step 2.2

Factor $2 x^{\frac{2}{3}}$ out of $- 2 x$ .

$2 x^{\frac{2}{3}} (3) + 2 x^{\frac{2}{3}} (- x^{\frac{1}{3}}) = 0$

Step 2.3

Factor $2 x^{\frac{2}{3}}$ out of $2 x^{\frac{2}{3}} (3) + 2 x^{\frac{2}{3}} (- x^{\frac{1}{3}})$ .

$2 x^{\frac{2}{3}} (3 - x^{\frac{1}{3}}) = 0$

Step 3

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x^{\frac{2}{3}} = 0$

$3 - x^{\frac{1}{3}} = 0$

Step 4

Set $x^{\frac{2}{3}}$ equal to $0$ and solve for $x$ .

Tap for more steps...

Step 4.1

Set $x^{\frac{2}{3}}$ equal to $0$ .

$x^{\frac{2}{3}} = 0$

Step 4.2

Solve $x^{\frac{2}{3}} = 0$ for $x$ .

Tap for more steps...

Step 4.2.1

Raise each side of the equation to the power of $\frac{3}{2}$ to eliminate the fractional exponent on the left side.

${(x^{\frac{2}{3}})}^{\frac{3}{2}} = \pm 0^{\frac{3}{2}}$

Step 4.2.2

Simplify the exponent.

Tap for more steps...

Step 4.2.2.1

Simplify the left side.

Tap for more steps...

Step 4.2.2.1.1

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

Tap for more steps...

Step 4.2.2.1.1.1

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

Tap for more steps...

Step 4.2.2.1.1.1.1

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

$x^{\frac{2}{3} \cdot \frac{3}{2}} = \pm 0^{\frac{3}{2}}$

Step 4.2.2.1.1.1.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 4.2.2.1.1.1.2.1

Cancel the common factor.

$x^{\frac{2}{3} \cdot \frac{3}{2}} = \pm 0^{\frac{3}{2}}$

Step 4.2.2.1.1.1.2.2

Rewrite the expression.

$x^{\frac{1}{3} \cdot 3} = \pm 0^{\frac{3}{2}}$

Step 4.2.2.1.1.1.3

Cancel the common factor of $3$ .

Tap for more steps...

Step 4.2.2.1.1.1.3.1

Cancel the common factor.

$x^{\frac{1}{3} \cdot 3} = \pm 0^{\frac{3}{2}}$

Step 4.2.2.1.1.1.3.2

Rewrite the expression.

$x^{1} = \pm 0^{\frac{3}{2}}$

Step 4.2.2.1.1.2

Simplify.

$x = \pm 0^{\frac{3}{2}}$

Step 4.2.2.2

Simplify the right side.

Tap for more steps...

Step 4.2.2.2.1

Simplify $\pm 0^{\frac{3}{2}}$ .

Tap for more steps...

Step 4.2.2.2.1.1

Simplify the expression.

Tap for more steps...

Step 4.2.2.2.1.1.1

Rewrite $0$ as $0^{2}$ .

$x = \pm {(0^{2})}^{\frac{3}{2}}$

Step 4.2.2.2.1.1.2

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

$x = \pm 0^{2 (\frac{3}{2})}$

Step 4.2.2.2.1.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 4.2.2.2.1.2.1

Cancel the common factor.

$x = \pm 0^{2 (\frac{3}{2})}$

Step 4.2.2.2.1.2.2

Rewrite the expression.

$x = \pm 0^{3}$

Step 4.2.2.2.1.3

Raising $0$ to any positive power yields $0$ .

$x = \pm 0$

Step 4.2.2.2.1.4

Plus or minus $0$ is $0$ .

$x = 0$

Step 5

Set $3 - x^{\frac{1}{3}}$ equal to $0$ and solve for $x$ .

Tap for more steps...

Step 5.1

Set $3 - x^{\frac{1}{3}}$ equal to $0$ .

$3 - x^{\frac{1}{3}} = 0$

Step 5.2

Solve $3 - x^{\frac{1}{3}} = 0$ for $x$ .

Tap for more steps...

Step 5.2.1

Subtract $3$ from both sides of the equation.

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

Step 5.2.2

Raise each side of the equation to the power of $3$ to eliminate the fractional exponent on the left side.

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

Step 5.2.3

Simplify the exponent.

Tap for more steps...

Step 5.2.3.1

Simplify the left side.

Tap for more steps...

Step 5.2.3.1.1

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

Tap for more steps...

Step 5.2.3.1.1.1

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

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

Step 5.2.3.1.1.2

Raise $- 1$ to the power of $3$ .

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

Step 5.2.3.1.1.3

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

Tap for more steps...

Step 5.2.3.1.1.3.1

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

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

Step 5.2.3.1.1.3.2

Cancel the common factor of $3$ .

Tap for more steps...

Step 5.2.3.1.1.3.2.1

Cancel the common factor.

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

Step 5.2.3.1.1.3.2.2

Rewrite the expression.

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

Step 5.2.3.1.1.4

Simplify.

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

Step 5.2.3.2

Simplify the right side.

Tap for more steps...

Step 5.2.3.2.1

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

$- x = - 27$

Step 5.2.4

Divide each term in $- x = - 27$ by $- 1$ and simplify.

Tap for more steps...

Step 5.2.4.1

Divide each term in $- x = - 27$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 27}{- 1}$

Step 5.2.4.2

Simplify the left side.

Tap for more steps...

Step 5.2.4.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 27}{- 1}$

Step 5.2.4.2.2

Divide $x$ by $1$ .

$x = \frac{- 27}{- 1}$

Step 5.2.4.3

Simplify the right side.

Tap for more steps...

Step 5.2.4.3.1

Divide $- 27$ by $- 1$ .

$x = 27$

Step 6

The final solution is all the values that make $2 x^{\frac{2}{3}} (3 - x^{\frac{1}{3}}) = 0$ true.

$x = 0, 27$