Question

What is the value of c in the equation below?

Answer 1

1/4

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