What is the value of c in the equation below?

1/4

Step-by-step explanation:

Let's find the value of c.

                              1         2^2        1

2^(-4)*2^2 = c = * = = 1/4

                             2^4          1         2^2

this result matches the fourth given possible answer choice.

For this case we have that by definition of power properties:

We have the following expression:

It can be rewritten as:

By definition of power properties we have:

So:

Thus,

Option D

3. parallelogram

step-by-step explanation:

we turn each of our sides into direction vectors

ab=b-a=(3 - 7, 1 - 0) = (-4, 1)

bc=c-b=(1,6)

cd=d-c=(4,-1)

da=a-d=(-1,-6)

we see how the opposite sides have negated direction vectors; this is characteristic of a parallelogram.   we have congruent sides ab=cd and bc=da with unequal lengths because 1^2+6^2 is different from (-4)^2+1^2.   so it's not a square or a rhombus.  

we check the dot product of direction vectors of adjacent sides.   we have

ab dot bc = -4(1) + 1(6) = 2

that's not zero so the sides are not perpendicular.   we've ruled out rectangle.

the direction vectors indicate two pairs of congruent parallel sides, so we choose parallelogram over trapezoid.