(numeratorx^-4y^2/Denominator x^-2y^-4)-3

You've given us a formula, but not given us what we are supposed to be doing with it...

the expression needs to be simplified

I tried

Oh! Okay, well anything to the negative power is equal to the reciprocal to the same positive power. Therefore;

(x^-4*y^2/x^-2*y^-4)^-3
= (x^-2*y^-4/x^-4*y^2)^3

You can then multiply each exponent within the brackets by 3. And simplify your numerator and denominator from there...

Let me know if you still need a hand!

To evaluate the expression (numeratorx^-4y^2/denominator x^-2y^-4)-3, we need to simplify it step by step.

Let's start by simplifying the numerator and the denominator separately.

In the numerator, we have x^-4y^2.
To simplify x^-4, we can rewrite it as 1/x^4 using the negative exponent rule, which states that x^-n is equal to 1/x^n.
The numerator becomes 1/(x^4)y^2.

In the denominator, we have x^-2y^-4.
Using the negative exponent rule again, x^-2 can be rewritten as 1/x^2, and y^-4 can be rewritten as 1/y^4.
The denominator becomes (1/x^2)(1/y^4).

Now that we have simplified the numerator and the denominator, we can rewrite the expression as (1/(x^4)y^2) / ((1/x^2)(1/y^4)) - 3.

To divide fractions, we multiply the numerator of the first fraction by the reciprocal of the second fraction. So, we can rewrite the expression as (1/(x^4)y^2) * (y^4/x^2) - 3.

When we multiply fractions, we multiply the numerators together and the denominators together. So, the expression becomes (y^4)/(x^6y^2) - 3.

Now, we can simplify further by combining the terms with the same base.

The first term (y^4)/(x^6y^2) can be simplified by dividing y^4 by y^2. The result is y^2.

The expression is now (y^2)/(x^6) - 3.

At this point, we can't simplify the expression any further because the terms have different bases. Therefore, the final answer to the expression (numeratorx^-4y^2/denominator x^-2y^-4)-3 is (y^2)/(x^6) - 3.