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

Answer 1

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

Answer 2

i dont understand

Answer 3

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!