Question

What is (-4)⁻³+(-4)⁻²+(-4)⁻¹+(-4)⁰+(-4)⁻¹+(-4)⁻²? express your answer as a fraction.

Answer 1

To solve this expression, evaluate each term separately and then add them together.

The answer is 39/64 as a fraction.

Step-by-step explanation:

To solve this expression, let's break it down step by step:

1. The first term, (-4)⁻³, can be rewritten as 1/(-4)³. This simplifies to -1/64.
2. The second term, (-4)⁻², is equivalent to 1/(-4)², which simplifies to 1/16.
3. The third term, (-4)⁻¹, is equal to 1/(-4), which simplifies to -1/4.
4. The fourth term, (-4)⁰, is always equal to 1.
5. For the fifth term, (-4)⁻¹, we already calculated it as -1/4.
6. The sixth term, (-4)⁻², is the same as 1/16.

Now, let's add all the terms together: (-1/64) + (1/16) + (-1/4) + 1 + (-1/4) + (1/16)

Simplifying the expression, we get: -1/64 + 4/64 - 16/64 + 64/64 - 16/64 + 4/64

= 39/64.

Therefore, the answer is 39/64 as a fraction.