Question

What is the value of the expression%C2%A0 (−5)−3 ? 1. Apply the negative exponent rule:%C2%A0 (−5)−3=1(−5)3 2. Expand the power:%C2%A0 (−5)−3=1(−5)3=1(−5)(−5)(−5) 3. Simplify:%C2%A0 (−5)−3=1(−5)3=1(−5)(−5)(−5)=1x What is the value of%C2%A0x? (1 point) Responses x=−15 x is equal to negative 15 x=125 x is equal to 125 x=15 x is equal to 15 x=−125 x is equal to negative 125

Answer 1

To find the value of the expression \((-5)^{-3}\), we can follow the steps outlined in your question.

1. **Apply the negative exponent rule**:
\[
(-5)^{-3} = \frac{1}{(-5)^3}
\]

2. **Expand the power**:
\[
(-5)^{-3} = \frac{1}{(-5)^3} = \frac{1}{(-5)(-5)(-5)}
\]

3. **Simplify**:
Now we need to calculate \((-5)(-5)(-5)\):
- First, calculate \((-5)(-5) = 25\).
- Then, calculate \(25 \times (-5) = -125\).

Therefore, \((-5)^3 = -125\).

Putting it back into our expression:
\[
(-5)^{-3} = \frac{1}{-125} = -\frac{1}{125}
\]

Now we have:
\[
x = -125
\]

Thus, the correct response is:
- \(x = -125\) (x is equal to negative 125).