Apply the product rule to <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><mn>9</mn></mrow></mfrac></mstyle></math> .

One to any power is one.

Move <math><mstyle displaystyle="true"><msup><mrow><mn>9</mn></mrow><mrow><mi>a</mi><mo>+</mo><mn>1</mn></mrow></msup></mstyle></math> to the numerator using the negative exponent rule <math><mstyle displaystyle="true"><mfrac><mrow><mn>1</mn></mrow><mrow><msup><mrow><mi>b</mi></mrow><mrow><mo>-</mo><mi>n</mi></mrow></msup></mrow></mfrac><mo>=</mo><msup><mrow><mi>b</mi></mrow><mrow><mi>n</mi></mrow></msup></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mn>81</mn></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>3</mn></mrow><mrow><mn>4</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> .

Apply the distributive property.

Multiply <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Rewrite <math><mstyle displaystyle="true"><mn>27</mn></mstyle></math> as <math><mstyle displaystyle="true"><msup><mrow><mn>3</mn></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> .

Apply the distributive property.

Multiply <math><mstyle displaystyle="true"><mn>3</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>3</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.

Subtract <math><mstyle displaystyle="true"><mn>3</mn><mi>a</mi></mstyle></math> from <math><mstyle displaystyle="true"><mn>4</mn><mi>a</mi></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>4</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>6</mn></mstyle></math> .

Create equivalent expressions in the equation that all have equal bases.

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

Simplify <math><mstyle displaystyle="true"><mn>2</mn><mrow><mo>(</mo><mo>-</mo><mrow><mo>(</mo><mi>a</mi><mo>+</mo><mn>1</mn><mo>)</mo></mrow><mo>)</mo></mrow></mstyle></math> .

Apply the distributive property.

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Apply the distributive property.

Multiply.

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> .

Move all terms containing <math><mstyle displaystyle="true"><mi>a</mi></mstyle></math> to the left side of the equation.

Subtract <math><mstyle displaystyle="true"><mi>a</mi></mstyle></math> from both sides of the equation.

Subtract <math><mstyle displaystyle="true"><mi>a</mi></mstyle></math> from <math><mstyle displaystyle="true"><mo>-</mo><mn>2</mn><mi>a</mi></mstyle></math> .

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

Add <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> to both sides of the equation.

Add <math><mstyle displaystyle="true"><mn>10</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>2</mn></mstyle></math> .

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

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

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

Cancel the common factor.

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

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

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