Question

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

Answer 1

To determine the value of \( x \) from the expression \((-5)^{-3}\), we can follow the steps you outlined:

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

2. **Expand the power**:
\[
(-5)^3 = (-5) \times (-5) \times (-5)
\]

3. **Calculate \((-5)^3\)**:
\[
(-5) \times (-5) = 25
\]
\[
25 \times (-5) = -125
\]
Thus, \((-5)^3 = -125\).

4. **Substituting back into the equation**:
\[
(-5)^{-3} = \frac{1}{-125}
\]

So, we have:
\[
(-5)^{-3} = -\frac{1}{125}
\]

Since the question asks for the value of \( x \) in your expansion, we can conclude that:
\[
x = -125
\]

Thus, the answer is:

**x = −125**.