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What is the value of c in the equation below?

What is the value of c in the equation below?-example-1
User Skaue
by
8.6k points

2 Answers

4 votes

Answer:

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.

User Tejs
by
7.7k points
2 votes

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

User Vaiden
by
7.4k points

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