Rewrite the equation as <math><mstyle displaystyle="true"><msup><mrow><mn>10</mn></mrow><mrow><mi>v</mi><mo>+</mo><mn>4</mn></mrow></msup><mo>⋅</mo><msup><mrow><mn>10</mn></mrow><mrow><mn>2</mn><mi>v</mi><mo>-</mo><mn>11</mn></mrow></msup><mo>=</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>-</mo><mn>4</mn></mrow></msup><mo>⋅</mo><msup><mrow><mn>10</mn></mrow><mrow><mn>9</mn></mrow></msup></mstyle></math> .

Use the power rule <math><mstyle displaystyle="true"><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi></mrow></msup><msup><mrow><mi>a</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>=</mo><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi><mo>+</mo><mi>n</mi></mrow></msup></mstyle></math> to combine exponents.

Add <math><mstyle displaystyle="true"><mi>v</mi></mstyle></math> and <math><mstyle displaystyle="true"><mn>2</mn><mi>v</mi></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mn>11</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> .

Use the power rule <math><mstyle displaystyle="true"><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi></mrow></msup><msup><mrow><mi>a</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>=</mo><msup><mrow><mi>a</mi></mrow><mrow><mi>m</mi><mo>+</mo><mi>n</mi></mrow></msup></mstyle></math> to combine exponents.

Add <math><mstyle displaystyle="true"><mo>-</mo><mn>4</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>9</mn></mstyle></math> .

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

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

Add <math><mstyle displaystyle="true"><mn>7</mn></mstyle></math> to both sides of the equation.

Add <math><mstyle displaystyle="true"><mn>5</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>7</mn></mstyle></math> .

Divide each term in <math><mstyle displaystyle="true"><mn>3</mn><mi>v</mi><mo>=</mo><mn>12</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>v</mi><mo>=</mo><mn>12</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>v</mi></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Simplify the right side.

Divide <math><mstyle displaystyle="true"><mn>12</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> .

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