Pre-Algebra Examples

${(x - 5)}^{\frac{2}{3}} = 4$

Step 1

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

${({(x - 5)}^{\frac{2}{3}})}^{\frac{3}{2}} = \pm 4^{\frac{3}{2}}$

Step 2

Simplify the exponent.

Tap for more steps...

Step 2.1

Simplify the left side.

Tap for more steps...

Step 2.1.1

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

Tap for more steps...

Step 2.1.1.1

Multiply the exponents in ${({(x - 5)}^{\frac{2}{3}})}^{\frac{3}{2}}$ .

Tap for more steps...

Step 2.1.1.1.1

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

${(x - 5)}^{\frac{2}{3} \cdot \frac{3}{2}} = \pm 4^{\frac{3}{2}}$

Step 2.1.1.1.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.1.1.1.2.1

Cancel the common factor.

${(x - 5)}^{\frac{2}{3} \cdot \frac{3}{2}} = \pm 4^{\frac{3}{2}}$

Step 2.1.1.1.2.2

Rewrite the expression.

${(x - 5)}^{\frac{1}{3} \cdot 3} = \pm 4^{\frac{3}{2}}$

Step 2.1.1.1.3

Cancel the common factor of $3$ .

Tap for more steps...

Step 2.1.1.1.3.1

Cancel the common factor.

${(x - 5)}^{\frac{1}{3} \cdot 3} = \pm 4^{\frac{3}{2}}$

Step 2.1.1.1.3.2

Rewrite the expression.

${(x - 5)}^{1} = \pm 4^{\frac{3}{2}}$

Step 2.1.1.2

Simplify.

$x - 5 = \pm 4^{\frac{3}{2}}$

Step 2.2

Simplify the right side.

Tap for more steps...

Step 2.2.1

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

Tap for more steps...

Step 2.2.1.1

Simplify the expression.

Tap for more steps...

Step 2.2.1.1.1

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

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

Step 2.2.1.1.2

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

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

Step 2.2.1.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.2.1.2.1

Cancel the common factor.

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

Step 2.2.1.2.2

Rewrite the expression.

$x - 5 = \pm 2^{3}$

Step 2.2.1.3

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

$x - 5 = \pm 8$

Step 3

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

Tap for more steps...

Step 3.1

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

$x - 5 = 8$

Step 3.2

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

Tap for more steps...

Step 3.2.1

Add $5$ to both sides of the equation.

$x = 8 + 5$

Step 3.2.2

Add $8$ and $5$ .

$x = 13$

Step 3.3

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

$x - 5 = - 8$

Step 3.4

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

Tap for more steps...

Step 3.4.1

Add $5$ to both sides of the equation.

$x = - 8 + 5$

Step 3.4.2

Add $- 8$ and $5$ .

$x = - 3$

Step 3.5

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

$x = 13, - 3$