Algebra Examples

$4 {(3 x - 3)}^{\frac{2}{3}} = 36$

Step 1

Divide each term in $4 {(3 x - 3)}^{\frac{2}{3}} = 36$ by $4$ and simplify.

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Step 1.1

Divide each term in $4 {(3 x - 3)}^{\frac{2}{3}} = 36$ by $4$ .

$\frac{4 {(3 x - 3)}^{\frac{2}{3}}}{4} = \frac{36}{4}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor.

$\frac{4 {(3 x - 3)}^{\frac{2}{3}}}{4} = \frac{36}{4}$

Step 1.2.2

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

${(3 x - 3)}^{\frac{2}{3}} = \frac{36}{4}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Divide $36$ by $4$ .

${(3 x - 3)}^{\frac{2}{3}} = 9$

Step 2

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

${({(3 x - 3)}^{\frac{2}{3}})}^{\frac{3}{2}} = \pm 9^{\frac{3}{2}}$

Step 3

Simplify the exponent.

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Step 3.1

Simplify the left side.

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Step 3.1.1

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

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Step 3.1.1.1

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

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Step 3.1.1.1.1

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

${(3 x - 3)}^{\frac{2}{3} \cdot \frac{3}{2}} = \pm 9^{\frac{3}{2}}$

Step 3.1.1.1.2

Cancel the common factor of $2$ .

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Step 3.1.1.1.2.1

Cancel the common factor.

${(3 x - 3)}^{\frac{2}{3} \cdot \frac{3}{2}} = \pm 9^{\frac{3}{2}}$

Step 3.1.1.1.2.2

Rewrite the expression.

${(3 x - 3)}^{\frac{1}{3} \cdot 3} = \pm 9^{\frac{3}{2}}$

Step 3.1.1.1.3

Cancel the common factor of $3$ .

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Step 3.1.1.1.3.1

Cancel the common factor.

${(3 x - 3)}^{\frac{1}{3} \cdot 3} = \pm 9^{\frac{3}{2}}$

Step 3.1.1.1.3.2

Rewrite the expression.

${(3 x - 3)}^{1} = \pm 9^{\frac{3}{2}}$

Step 3.1.1.2

Simplify.

$3 x - 3 = \pm 9^{\frac{3}{2}}$

Step 3.2

Simplify the right side.

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Step 3.2.1

Simplify $\pm 9^{\frac{3}{2}}$ .

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Step 3.2.1.1

Simplify the expression.

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Step 3.2.1.1.1

Rewrite $9$ as $3^{2}$ .

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

Step 3.2.1.1.2

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

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

Step 3.2.1.2

Cancel the common factor of $2$ .

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Step 3.2.1.2.1

Cancel the common factor.

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

Step 3.2.1.2.2

Rewrite the expression.

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

Step 3.2.1.3

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

$3 x - 3 = \pm 27$

Step 4

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

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Step 4.1

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

$3 x - 3 = 27$

Step 4.2

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

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Step 4.2.1

Add $3$ to both sides of the equation.

$3 x = 27 + 3$

Step 4.2.2

Add $27$ and $3$ .

$3 x = 30$

Step 4.3

Divide each term in $3 x = 30$ by $3$ and simplify.

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Step 4.3.1

Divide each term in $3 x = 30$ by $3$ .

$\frac{3 x}{3} = \frac{30}{3}$

Step 4.3.2

Simplify the left side.

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Step 4.3.2.1

Cancel the common factor of $3$ .

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Step 4.3.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{30}{3}$

Step 4.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{30}{3}$

Step 4.3.3

Simplify the right side.

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Step 4.3.3.1

Divide $30$ by $3$ .

$x = 10$

Step 4.4

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

$3 x - 3 = - 27$

Step 4.5

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

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Step 4.5.1

Add $3$ to both sides of the equation.

$3 x = - 27 + 3$

Step 4.5.2

Add $- 27$ and $3$ .

$3 x = - 24$

Step 4.6

Divide each term in $3 x = - 24$ by $3$ and simplify.

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Step 4.6.1

Divide each term in $3 x = - 24$ by $3$ .

$\frac{3 x}{3} = \frac{- 24}{3}$

Step 4.6.2

Simplify the left side.

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Step 4.6.2.1

Cancel the common factor of $3$ .

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Step 4.6.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{- 24}{3}$

Step 4.6.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 24}{3}$

Step 4.6.3

Simplify the right side.

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Step 4.6.3.1

Divide $- 24$ by $3$ .

$x = - 8$

Step 4.7

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

$x = 10, - 8$