use the properties of eponts to simplfiy the expression below -2^-5

To simplify the expression \(-2^{-5}\), we can use the properties of exponents.

1. **Negative Exponent Rule**: According to this rule, \(a^{-n} = \frac{1}{a^n}\). Therefore, we can rewrite \(-2^{-5}\) as:
\[
-2^{-5} = -\frac{1}{2^5}
\]

2. **Calculate \(2^5\)**:
\[
2^5 = 32
\]

3. **Substituting back into the expression**:
\[
-\frac{1}{2^5} = -\frac{1}{32}
\]

So the simplified form of \(-2^{-5}\) is:
\[
-\frac{1}{32}
\]

i dont understand

No problem! Let’s break it down step-by-step in simpler terms.

We are starting with the expression:

\[
-2^{-5}
\]

### Step 1: Understanding the Negative Exponent

When you see a negative exponent, it means you should take the reciprocal of the base and change the exponent to positive. The rule is:

\[
a^{-n} = \frac{1}{a^n}
\]

In our case, the base is \(2\) and the exponent is \(5\). So:

\[
-2^{-5} = -\frac{1}{2^5}
\]

### Step 2: Calculate \(2^5\)

Now we need to find \(2^5\). This means multiplying \(2\) by itself \(5\) times:

\[
2^5 = 2 \times 2 \times 2 \times 2 \times 2
\]

Calculating this step-by-step:
- \(2 \times 2 = 4\)
- \(4 \times 2 = 8\)
- \(8 \times 2 = 16\)
- \(16 \times 2 = 32\)

So, \(2^5 = 32\).

### Step 3: Substitute Back

Now we can substitute \(32\) back into our expression:

\[
-2^{-5} = -\frac{1}{2^5} = -\frac{1}{32}
\]

### Conclusion

So the simplified version of \(-2^{-5}\) is:

\[
-\frac{1}{32}
\]

If you have more questions or would like me to explain further, feel free to ask!