# Solve for a (1/9)^(a+1)=81^(a+1)*27^(2-a)

Solve for a (1/9)^(a+1)=81^(a+1)*27^(2-a)
Apply the product rule to .
One to any power is one.
Move to the numerator using the negative exponent rule .
Rewrite as .
Multiply the exponents in .
Apply the power rule and multiply exponents, .
Apply the distributive property.
Multiply by .
Rewrite as .
Multiply the exponents in .
Apply the power rule and multiply exponents, .
Apply the distributive property.
Multiply by .
Multiply by .
Use the power rule to combine exponents.
Subtract from .
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.
Solve for .
Simplify .
Apply the distributive property.
Multiply by .
Apply the distributive property.
Multiply.
Multiply by .
Multiply by .
Move all terms containing to the left side of the equation.
Subtract from both sides of the equation.
Subtract from .
Move all terms not containing to the right side of the equation.
Add to both sides of the equation.