Pre-Algebra Examples

$7 {(z - 2)}^{\frac{2}{3}} = 56$

Step 1

Divide each term in $7 {(z - 2)}^{\frac{2}{3}} = 56$ by $7$ and simplify.

Tap for more steps...

Step 1.1

Divide each term in $7 {(z - 2)}^{\frac{2}{3}} = 56$ by $7$ .

$\frac{7 {(z - 2)}^{\frac{2}{3}}}{7} = \frac{56}{7}$

Step 1.2

Simplify the left side.

Tap for more steps...

Step 1.2.1

Cancel the common factor.

$\frac{7 {(z - 2)}^{\frac{2}{3}}}{7} = \frac{56}{7}$

Step 1.2.2

Divide ${(z - 2)}^{\frac{2}{3}}$ by $1$ .

${(z - 2)}^{\frac{2}{3}} = \frac{56}{7}$

Step 1.3

Simplify the right side.

Tap for more steps...

Step 1.3.1

Divide $56$ by $7$ .

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

Step 2

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

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

Step 3

Simplify the left side.

Tap for more steps...

Step 3.1

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

Tap for more steps...

Step 3.1.1

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

Tap for more steps...

Step 3.1.1.1

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

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

Step 3.1.1.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.1.1.2.1

Cancel the common factor.

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

Step 3.1.1.2.2

Rewrite the expression.

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

Step 3.1.1.3

Cancel the common factor of $3$ .

Tap for more steps...

Step 3.1.1.3.1

Cancel the common factor.

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

Step 3.1.1.3.2

Rewrite the expression.

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

Step 3.1.2

Simplify.

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

Step 4

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

Tap for more steps...

Step 4.1

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

$z - 2 = 8^{\frac{3}{2}}$

Step 4.2

Add $2$ to both sides of the equation.

$z = 8^{\frac{3}{2}} + 2$

Step 4.3

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

$z - 2 = - 8^{\frac{3}{2}}$

Step 4.4

Add $2$ to both sides of the equation.

$z = - 8^{\frac{3}{2}} + 2$

Step 4.5

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

$z = 8^{\frac{3}{2}} + 2, - 8^{\frac{3}{2}} + 2$