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