# Solve for x (1/5)^(x-2)=125^(x/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 .
Combine and .
Move all terms containing to the left side of the equation.
Subtract from both sides of the equation.
To write as a fraction with a common denominator, multiply by .
Combine and .
Combine the numerators over the common denominator.
Simplify each term.
Simplify the numerator.
Factor out of .
Factor out of .
Factor out of .
Factor out of .
Multiply by .
Subtract from .
Move to the left of .
Move the negative in front of the fraction.
Subtract from both sides of the equation.
Multiply both sides of the equation by .
Simplify both sides of the equation.
Simplify .
Cancel the common factor of .
Move the leading negative in into the numerator.
Move the leading negative in into the numerator.
Factor out of .
Cancel the common factor.
Rewrite the expression.
Cancel the common factor of .
Factor out of .
Cancel the common factor.
Rewrite the expression.
Multiply.
Multiply by .
Multiply by .
Multiply .
Multiply by .
Combine and .
Multiply by .
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
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