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 .

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:

Solve for x (1/5)^(x-2)=125^(x/2)