Algebra Examples

$5 {(2 x - 1)}^{\frac{2}{3}} = 125$

Step 1

Divide each term in $5 {(2 x - 1)}^{\frac{2}{3}} = 125$ by $5$ and simplify.

Tap for more steps...

Step 1.1

Divide each term in $5 {(2 x - 1)}^{\frac{2}{3}} = 125$ by $5$ .

$\frac{5 {(2 x - 1)}^{\frac{2}{3}}}{5} = \frac{125}{5}$

Step 1.2

Simplify the left side.

Tap for more steps...

Step 1.2.1

Cancel the common factor.

$\frac{5 {(2 x - 1)}^{\frac{2}{3}}}{5} = \frac{125}{5}$

Step 1.2.2

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

${(2 x - 1)}^{\frac{2}{3}} = \frac{125}{5}$

Step 1.3

Simplify the right side.

Tap for more steps...

Step 1.3.1

Divide $125$ by $5$ .

${(2 x - 1)}^{\frac{2}{3}} = 25$

Step 2

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

${({(2 x - 1)}^{\frac{2}{3}})}^{\frac{3}{2}} = \pm 25^{\frac{3}{2}}$

Step 3

Simplify the exponent.

Tap for more steps...

Step 3.1

Simplify the left side.

Tap for more steps...

Step 3.1.1

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

Tap for more steps...

Step 3.1.1.1

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

Tap for more steps...

Step 3.1.1.1.1

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

${(2 x - 1)}^{\frac{2}{3} \cdot \frac{3}{2}} = \pm 25^{\frac{3}{2}}$

Step 3.1.1.1.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.1.1.1.2.1

Cancel the common factor.

${(2 x - 1)}^{\frac{2}{3} \cdot \frac{3}{2}} = \pm 25^{\frac{3}{2}}$

Step 3.1.1.1.2.2

Rewrite the expression.

${(2 x - 1)}^{\frac{1}{3} \cdot 3} = \pm 25^{\frac{3}{2}}$

Step 3.1.1.1.3

Cancel the common factor of $3$ .

Tap for more steps...

Step 3.1.1.1.3.1

Cancel the common factor.

${(2 x - 1)}^{\frac{1}{3} \cdot 3} = \pm 25^{\frac{3}{2}}$

Step 3.1.1.1.3.2

Rewrite the expression.

${(2 x - 1)}^{1} = \pm 25^{\frac{3}{2}}$

Step 3.1.1.2

Simplify.

$2 x - 1 = \pm 25^{\frac{3}{2}}$

Step 3.2

Simplify the right side.

Tap for more steps...

Step 3.2.1

Simplify $\pm 25^{\frac{3}{2}}$ .

Tap for more steps...

Step 3.2.1.1

Simplify the expression.

Tap for more steps...

Step 3.2.1.1.1

Rewrite $25$ as $5^{2}$ .

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

Step 3.2.1.1.2

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

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

Step 3.2.1.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.2.1.2.1

Cancel the common factor.

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

Step 3.2.1.2.2

Rewrite the expression.

$2 x - 1 = \pm 5^{3}$

Step 3.2.1.3

Raise $5$ to the power of $3$ .

$2 x - 1 = \pm 125$

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.

$2 x - 1 = 125$

Step 4.2

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

Tap for more steps...

Step 4.2.1

Add $1$ to both sides of the equation.

$2 x = 125 + 1$

Step 4.2.2

Add $125$ and $1$ .

$2 x = 126$

Step 4.3

Divide each term in $2 x = 126$ by $2$ and simplify.

Tap for more steps...

Step 4.3.1

Divide each term in $2 x = 126$ by $2$ .

$\frac{2 x}{2} = \frac{126}{2}$

Step 4.3.2

Simplify the left side.

Tap for more steps...

Step 4.3.2.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 4.3.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{126}{2}$

Step 4.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{126}{2}$

Step 4.3.3

Simplify the right side.

Tap for more steps...

Step 4.3.3.1

Divide $126$ by $2$ .

$x = 63$

Step 4.4

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

$2 x - 1 = - 125$

Step 4.5

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

Tap for more steps...

Step 4.5.1

Add $1$ to both sides of the equation.

$2 x = - 125 + 1$

Step 4.5.2

Add $- 125$ and $1$ .

$2 x = - 124$

Step 4.6

Divide each term in $2 x = - 124$ by $2$ and simplify.

Tap for more steps...

Step 4.6.1

Divide each term in $2 x = - 124$ by $2$ .

$\frac{2 x}{2} = \frac{- 124}{2}$

Step 4.6.2

Simplify the left side.

Tap for more steps...

Step 4.6.2.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 4.6.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 124}{2}$

Step 4.6.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 124}{2}$

Step 4.6.3

Simplify the right side.

Tap for more steps...

Step 4.6.3.1

Divide $- 124$ by $2$ .

$x = - 62$

Step 4.7

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

$x = 63, - 62$