Apply the product rule to .

One to any power is one.

Move to the numerator using the negative exponent rule .

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.

Multiply each term in by

Multiply each term in by .

Simplify .

Apply the distributive property.

Multiply by .

Apply the distributive property.

Multiply .

Multiply by .

Multiply by .

Multiply by .

Multiply by .

Move all terms not containing to the right side of the equation.

Add to both sides of the equation.

Add and .

Solve for x (1/27)^(x-6)=27