Multiply and simplify as indicated.

numerator x divided by denominator x to the 2 power negative 2x times numerator 27x negative 54 divided by denominator 15x

To multiply and simplify the given expression, we need to follow these steps:

Step 1: Simplify the fractions individually.
Step 2: Multiply the numerators together to get the new numerator.
Step 3: Multiply the denominators together to get the new denominator.
Step 4: Simplify the resulting fraction (if possible) by canceling out any common factors between the numerator and denominator.

Let's apply these steps to the given expression:

The given expression is (numerator x / denominator x^(-2x)) * (numerator 27x - 54 / denominator 15x).

Step 1: Simplify the fractions individually.
The first fraction, (numerator x / denominator x^(-2x)), can be simplified using the negative exponent rule. A negative exponent in the denominator can be moved to the numerator and made positive. Therefore, x^(-2x) becomes 1 / x^(2x).

The second fraction, (numerator 27x - 54 / denominator 15x), is already in its simplified form.

After simplifying, the expression becomes (numerator x / 1 / x^(2x)) * (numerator 27x - 54 / denominator 15x).

Step 2: Multiply the numerators together.
The numerators to multiply are x * (27x - 54).

Step 3: Multiply the denominators together.
The denominators to multiply are (1 / x^(2x)) * 15x.

After multiplying, the expression becomes (x * (27x - 54)) / (15x / x^(2x)).

Step 4: Simplify the resulting fraction.
To simplify further, let's simplify the denominator first. When dividing fractions, we can rewrite the division as multiplication by the reciprocal of the denominator. Therefore, (15x / x^(2x)) becomes (15x * x^(-2x)). To multiply this, we add the exponents, so it becomes 15x * 1 / x^(2x) = 15 / x^(2x-1).

Now our expression becomes (x * (27x - 54)) / (15 / x^(2x-1)).

To simplify the numerator, distribute x through (27x - 54). So it simplifies to (27x^2 - 54x).

Finally, we have (27x^2 - 54x) / (15 / x^(2x-1)) as the simplified expression.

Please note that I assumed there was an error in your question and that the term "numerator" and "denominator" were used incorrectly.