d. −7/32
Step-by-step explanation:
The expression that we have to evaluate in this problem is:
![7x^{-3}y^{-1}](/tpl/images/0529/1659/ad9ec.png)
We have to evaluate this expression for:
x = -2
y = 4
We start by rewriting the expression by rewriting it using the following:
![a^{-n}=\frac{1}{a^n}](/tpl/images/0529/1659/5f9fb.png)
So the expression can be rewritten as
![7x^{-3}y^{-1}=\frac{7}{x^3 y}](/tpl/images/0529/1659/8bd28.png)
Now we observe that:
![(-2)^3=(-2)(-2)(-2)=-8](/tpl/images/0529/1659/35469.png)
Therefore, by substituting x = -2 and y = 4 into the expression, we find:
![\frac{7}{(-2)^3\cdot 4}=\frac{7}{-8\cdot 4}=-\frac{7}{32}](/tpl/images/0529/1659/b51c9.png)