Solve for x (2x-8)^(2/3)=4

${(2 x - 8)}^{\frac{2}{3}} = 4$

Step 1

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

${({(2 x - 8)}^{\frac{2}{3}})}^{\frac{3}{2}} = \pm 4^{\frac{3}{2}}$

Step 2

Simplify the exponent.

Simplify the left side.

Simplify ${({(2 x - 8)}^{\frac{2}{3}})}^{\frac{3}{2}}$ .

Multiply the exponents in ${({(2 x - 8)}^{\frac{2}{3}})}^{\frac{3}{2}}$ .

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

${(2 x - 8)}^{\frac{2}{3} \cdot \frac{3}{2}} = \pm 4^{\frac{3}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(2 x - 8)}^{\frac{2}{3} \cdot \frac{3}{2}} = \pm 4^{\frac{3}{2}}$

Rewrite the expression.

${(2 x - 8)}^{\frac{1}{3} \cdot 3} = \pm 4^{\frac{3}{2}}$

Cancel the common factor of $3$ .

Cancel the common factor.

${(2 x - 8)}^{\frac{1}{3} \cdot 3} = \pm 4^{\frac{3}{2}}$

Rewrite the expression.

${(2 x - 8)}^{1} = \pm 4^{\frac{3}{2}}$

Simplify.

$2 x - 8 = \pm 4^{\frac{3}{2}}$

Simplify the right side.

Simplify $\pm 4^{\frac{3}{2}}$ .

Simplify the expression.

Rewrite $4$ as $2^{2}$ .

$2 x - 8 = \pm {(2^{2})}^{\frac{3}{2}}$

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

$2 x - 8 = \pm 2^{2 (\frac{3}{2})}$

Cancel the common factor of $2$ .

Cancel the common factor.

$2 x - 8 = \pm 2^{2 (\frac{3}{2})}$

Rewrite the expression.

$2 x - 8 = \pm 2^{3}$

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

$2 x - 8 = \pm 8$

Step 3

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$2 x - 8 = 8$

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

Add $8$ to both sides of the equation.

$2 x = 8 + 8$

Add $8$ and $8$ .

$2 x = 16$

Divide each term in $2 x = 16$ by $2$ and simplify.

Divide each term in $2 x = 16$ by $2$ .

$\frac{2 x}{2} = \frac{16}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{16}{2}$

Divide $x$ by $1$ .

$x = \frac{16}{2}$

Simplify the right side.

Divide $16$ by $2$ .

$x = 8$

Next, use the negative value of the $\pm$ to find the second solution.

$2 x - 8 = - 8$

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

Add $8$ to both sides of the equation.

$2 x = - 8 + 8$

Add $- 8$ and $8$ .

$2 x = 0$

Divide each term in $2 x = 0$ by $2$ and simplify.

Divide each term in $2 x = 0$ by $2$ .

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $0$ by $2$ .

$x = 0$

The complete solution is the result of both the positive and negative portions of the solution.

$x = 8, 0$

Solve for x (2x-8)^(2/3)=4

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