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.

Simplify .

Apply the distributive property.

Multiply by .

Simplify .

Apply the distributive property.

Multiply.

Multiply by .

Multiply by .

Move all terms containing to the left side of the equation.

Add to both sides of the equation.

Add and .

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

Add to both sides of the equation.

Add and .

Divide each term by and simplify.

Divide each term in by .

Cancel the common factor of .

Cancel the common factor.

Divide by .

The result can be shown in multiple forms.

Exact Form:

Decimal Form:

Solve for x 8^(x-1)=(1/2)^(2x-1)