Rewrite the equation as <math><mstyle displaystyle="true"><mn>7</mn><msup><mrow><mi>x</mi></mrow><mrow><mn>4</mn></mrow></msup><mo>=</mo><mn>199927</mn></mstyle></math> .

Divide each term in <math><mstyle displaystyle="true"><mn>7</mn><msup><mrow><mi>x</mi></mrow><mrow><mn>4</mn></mrow></msup><mo>=</mo><mn>199927</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>7</mn></mstyle></math> .

Simplify the left side.

Cancel the common factor of <math><mstyle displaystyle="true"><mn>7</mn></mstyle></math> .

Cancel the common factor.

Divide <math><mstyle displaystyle="true"><msup><mrow><mi>x</mi></mrow><mrow><mn>4</mn></mrow></msup></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Simplify the right side.

Divide <math><mstyle displaystyle="true"><mn>199927</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>7</mn></mstyle></math> .

Take the 4th root of both sides of the equation to eliminate the exponent on the left side.

Rewrite <math><mstyle displaystyle="true"><mn>28561</mn></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>13</mn></mrow><mrow><mn>4</mn></mrow></msup></mstyle></math> .

Pull terms out from under the radical, assuming positive real numbers.

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

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

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

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