Divide each term in <math><mstyle displaystyle="true"><mn>4</mn><msup><mrow><mo>(</mo><mn>3</mn><mi>x</mi><mo>-</mo><mn>3</mn><mo>)</mo></mrow><mrow><mfrac><mrow><mn>2</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mrow></msup><mo>=</mo><mn>36</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> .

Simplify the left side.

Cancel the common factor.

Divide <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><mn>3</mn><mi>x</mi><mo>-</mo><mn>3</mn><mo>)</mo></mrow><mrow><mfrac><mrow><mn>2</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mrow></msup></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Simplify the right side.

Divide <math><mstyle displaystyle="true"><mn>36</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> .

Raise each side of the equation to the power of <math><mstyle displaystyle="true"><mfrac><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mstyle></math> to eliminate the fractional exponent on the left side.

Simplify the left side.

Simplify <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><msup><mrow><mo>(</mo><mn>3</mn><mi>x</mi><mo>-</mo><mn>3</mn><mo>)</mo></mrow><mrow><mfrac><mrow><mn>2</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mrow></msup><mo>)</mo></mrow><mrow><mfrac><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup></mstyle></math> .

Multiply the exponents in <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><msup><mrow><mo>(</mo><mn>3</mn><mi>x</mi><mo>-</mo><mn>3</mn><mo>)</mo></mrow><mrow><mfrac><mrow><mn>2</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mrow></msup><mo>)</mo></mrow><mrow><mfrac><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup></mstyle></math> .

Apply the power rule and multiply exponents, <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi></mrow></msup><mo>)</mo></mrow><mrow><mi>n</mi></mrow></msup><mo>=</mo><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi><mi>n</mi></mrow></msup></mstyle></math> .

Cancel the common factor of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Cancel the common factor of <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Simplify.

Simplify the right side.

Simplify <math><mstyle displaystyle="true"><mo>±</mo><msup><mrow><mn>9</mn></mrow><mrow><mfrac><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup></mstyle></math> .

Simplify the expression.

Rewrite <math><mstyle displaystyle="true"><mn>9</mn></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>3</mn></mrow><mrow><mn>2</mn></mrow></msup></mstyle></math> .

Apply the power rule and multiply exponents, <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi></mrow></msup><mo>)</mo></mrow><mrow><mi>n</mi></mrow></msup><mo>=</mo><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi><mi>n</mi></mrow></msup></mstyle></math> .

Cancel the common factor of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Raise <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> .

First, use the positive value of the <math><mstyle displaystyle="true"><mo>±</mo></mstyle></math> to find the first solution.

Move all terms not containing <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> to the right side of the equation.

Add <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> to both sides of the equation.

Add <math><mstyle displaystyle="true"><mn>27</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> .

Divide each term in <math><mstyle displaystyle="true"><mn>3</mn><mi>x</mi><mo>=</mo><mn>30</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> and simplify.

Divide each term in <math><mstyle displaystyle="true"><mn>3</mn><mi>x</mi><mo>=</mo><mn>30</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> .

Simplify the left side.

Cancel the common factor of <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> .

Cancel the common factor.

Divide <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Simplify the right side.

Divide <math><mstyle displaystyle="true"><mn>30</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> .

Next, use the negative value of the <math><mstyle displaystyle="true"><mo>±</mo></mstyle></math> to find the second solution.

Move all terms not containing <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> to the right side of the equation.

Add <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> to both sides of the equation.

Add <math><mstyle displaystyle="true"><mo>-</mo><mn>27</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> .

Divide each term in <math><mstyle displaystyle="true"><mn>3</mn><mi>x</mi><mo>=</mo><mo>-</mo><mn>24</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> and simplify.

Divide each term in <math><mstyle displaystyle="true"><mn>3</mn><mi>x</mi><mo>=</mo><mo>-</mo><mn>24</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> .

Simplify the left side.

Cancel the common factor of <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> .

Cancel the common factor.

Divide <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Simplify the right side.

Divide <math><mstyle displaystyle="true"><mo>-</mo><mn>24</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> .

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

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