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 .

Apply the distributive property.

Multiply.

Multiply by .

Multiply by .

Add to both sides of the equation.

Move to the left side of the equation by subtracting it from both sides.

Combine the opposite terms in .

Subtract from .

Add and .

Factor out of .

Reorder and .

Factor out of .

Factor out of .

Factor out of .

Multiply each term in by

Multiply each term in by .

Simplify .

Apply the distributive property.

Simplify the expression.

Multiply by .

Multiply by .

Multiply by .

Apply the distributive property.

Multiply.

Multiply by .

Multiply by .

Multiply by .

Factor out of .

Factor out of .

Factor out of .

Factor out of .

Multiply each term in by

Multiply each term in by .

Simplify .

Apply the distributive property.

Simplify the expression.

Multiply by .

Multiply by .

Multiply by .

Apply the distributive property.

Multiply.

Multiply by .

Multiply by .

Multiply by .

Factor out of .

Factor out of .

Factor out of .

Factor out of .

If any individual factor on the left side of the equation is equal to , the entire expression will be equal to .

Set the first factor equal to .

Set the next factor equal to and solve.

Set the next factor equal to .

Add to both sides of the equation.

Divide each term by and simplify.

Divide each term in by .

Cancel the common factor of .

Cancel the common factor.

Divide by .

The final solution is all the values that make true.

The result can be shown in multiple forms.

Exact Form:

Decimal Form:

Mixed Number Form:

Solve for x (1/8)^(x-1)=2^(3-2x^2)