Can you check this:

x^-3y^2/x^2y^-4

I think the answer is y^6/x^5

Thanks for explaining the other problem

correct, good job

Thank you so much for your help

To simplify the expression (x^-3y^2)/(x^2y^-4), we can use the laws of exponents.

Start by simplifying the numerator, x^-3y^2.

Recall that when you have a negative exponent, you can move the base to the denominator by changing the sign of the exponent. So x^-3 can be rewritten as 1/x^3.

Now let's simplify the denominator, x^2y^-4.

Similarly, y^-4 can be rewritten as 1/y^4.

Now, substitute the simplified forms back into the expression:

(1/x^3)(y^2)/(x^2)(1/y^4).

Next, let's simplify the expression further.

In the numerator, multiply y^2 by 1 to get y^2.

In the denominator, multiply 1/x^2 by (1/y^4) to get 1/(x^2y^4).

Now, we can cancel out common factors.

There is an x^2 in the denominator of the numerator and the denominator of the denominator, so these can be canceled out, leaving:

(y^2)/(xy^4).

Now, we can simplify further by dividing y^2 by y^4.

When you divide variables with the same base, you subtract the exponents. So y^2/y^4 can be simplified to y^(-4 + 2), which is y^(-2).

Therefore, the final simplified expression is y^-2/x.

Recall that a negative exponent indicates that the base is in the denominator. So y^-2 can be rewritten as 1/y^2.

Therefore, the simplified expression is 1/y^2x.