Question

What is the value of 7 ^−3 ^ −1 for = −2 and = 4?
a. −224
b. 7/4096
c. 7(−8)^−4
d. −7/32

Answer 1

Answer:

d. −7/32

Step-by-step explanation:

The expression that we have to evaluate in this problem is:

$7x^{-3}y^{-1}$

We have to evaluate this expression for:

x = -2

y = 4

We start by rewriting the expression by rewriting it using the following:

$a^{-n}=\frac{1}{a^n}$

So the expression can be rewritten as

$7x^{-3}y^{-1}=\frac{7}{x^3 y}$

Now we observe that:

$(-2)^3=(-2)(-2)(-2)=-8$

Therefore, by substituting x = -2 and y = 4 into the expression, we find:

$\frac{7}{(-2)^3\cdot 4}=\frac{7}{-8\cdot 4}=-\frac{7}{32}$