To remove the radical on the left side of the equation, square both sides of the equation.

Use <math><mstyle displaystyle="true"><mroot><mrow><msup><mrow><mi>a</mi></mrow><mrow><mi>x</mi></mrow></msup></mrow><mrow><mi>n</mi></mrow></mroot><mo>=</mo><msup><mrow><mi>a</mi></mrow><mrow><mfrac><mrow><mi>x</mi></mrow><mrow><mi>n</mi></mrow></mfrac></mrow></msup></mstyle></math> to rewrite <math><mstyle displaystyle="true"><msqrt><mroot><mrow><mi>x</mi></mrow><mrow><mn>3</mn></mrow></mroot></msqrt></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mroot><mrow><mi>x</mi></mrow><mrow><mn>3</mn></mrow></mroot></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup></mstyle></math> .

Simplify the left side.

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

Multiply the exponents in <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><msup><mrow><mroot><mrow><mi>x</mi></mrow><mrow><mn>3</mn></mrow></mroot></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msup><mo>)</mo></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.

Simplify.

Simplify the right side.

Raise <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

To remove the radical on the left side of the equation, cube both sides of the equation.

Use <math><mstyle displaystyle="true"><mroot><mrow><msup><mrow><mi>a</mi></mrow><mrow><mi>x</mi></mrow></msup></mrow><mrow><mi>n</mi></mrow></mroot><mo>=</mo><msup><mrow><mi>a</mi></mrow><mrow><mfrac><mrow><mi>x</mi></mrow><mrow><mi>n</mi></mrow></mfrac></mrow></msup></mstyle></math> to rewrite <math><mstyle displaystyle="true"><mroot><mrow><mi>x</mi></mrow><mrow><mn>3</mn></mrow></mroot></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mi>x</mi></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mrow></msup></mstyle></math> .

Simplify the left side.

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

Multiply the exponents in <math><mstyle displaystyle="true"><msup><mrow><mo>(</mo><msup><mrow><mi>x</mi></mrow><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>3</mn></mrow></mfrac></mrow></msup><mo>)</mo></mrow><mrow><mn>3</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>3</mn></mstyle></math> .

Cancel the common factor.

Rewrite the expression.

Simplify.

Simplify the right side.

Raise <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> to the power of <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> .

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