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

d. −7/32

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)=(1)/(a^n)`

So the expression can be rewritten as

`7x^(-3)y^(-1)=(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:

`(7)/((-2)^3\cdot 4)=(7)/(-8\cdot 4)=-(7)/(32)`