If I had a math problem 2x^4 x y^-4 x z^-3 / 3x^2 x y^-3 x z^4.

In simpler terms it would look like this:
2x^4 X y^-4 X z^-3
-------------------
3x^2 X y^-3 X z^4

When I tried to solve this I got 6x^2 X y^-1 X 2^-7. Am I correct? If not could you please help me on how to solve it.

Nope. The coefficients just divide normally: 2/3

x^4/x^2 = x^2
y^-4/y^-3 = y^-1
z^-3/z^4 = z^-7

so, you wind up with

2/3 x^2 y^-1 z^-7, or

2x^2
--------
3yz^7

To simplify the given expression, we can combine similar terms in the numerator and the denominator by applying the laws of exponents. Let's break it down step by step:

First, let's simplify the numbers in the expression. We have:

2 / 3 = 2/3

Next, we can simplify the variables with exponents in the numerator and the denominator.

For the x terms:
x^4 / x^2 = x^(4-2) = x^2

For the y terms:
y^-4 / y^-3 = y^(-4+3) = y^-1 = 1/y

For the z terms:
z^-3 / z^4 = z^(-3-4) = z^-7 = 1/z^7

Combining the simplified terms, we have:

(2/3)(x^2)(1/y)(1/z^7)

So the final simplified expression is:
2x^2 / (3yz^7)

The result you obtained, 6x^2y^-1z^-7, is not correct. You missed the step of converting 2 into the fraction 2/3.

Therefore, the correct simplified form of the expression is 2x^2 / (3yz^7).