Question

What is the value of c in the equation below?

Answer 1

Answer:

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.

Answer 2

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

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

We have the following expression:

$2 ^ {- 4} * 2 ^ 2 = a ^ b = c$

It can be rewritten as:

$\frac {2 ^ 2} {2 ^ 4}$

By definition of power properties we have:

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

So:

$\frac {2 ^ 2} {2 ^ 4} = 2 ^ {2-4} = 2 ^ {- 2} = \frac {1} {2 ^ 2} = \frac {1} {4}$

Thus, $c = \frac {1} {4}$

Answer:

Option D