By using properties for exponents, we will see that the equivalent expression is:
[tex]2x^{-4}y^6[/tex]
Which is the equivalent expression?
Here you need to remember the property:
[tex]a^n/a^m = a^{n - m}[/tex]
We have the expression:
[tex]\frac{-4x^{-3}y^4}{-2xy^{-2}}[/tex]
We can separate the fraction to:
[tex]\frac{-4x^{-3}y^4}{-2xy^{-2}} = \frac{-4}{-2}*\frac{x^{-3}}{x} *\frac{y^4}{y^{-2}}[/tex]
Now we can simplify by using the above relation, we will get:
[tex]\frac{-4x^{-3}y^4}{-2xy^{-2}} = \frac{-4}{-2}*\frac{x^{-3}}{x} *\frac{y^4}{y^{-2}} = 2*x^{-3-1}*y^{4 - (2)} = 2*x^{-4}*y^6[/tex]
So the correct option is the last one.
If you want to learn more about exponents, you can read:
https://brainly.com/question/8952483
