What is the value of the expression (−5)−3

Question

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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)
Responses

x=15
x is equal to 15

x=−15
x is equal to negative 15

x=−125
x is equal to negative 125

x=125

Answer 1

To calculate the value of \((-5)^{-3}\), 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 \((-5) \times (-5)\): \[ (-5) \times (-5) = 25 \]

4. Next, multiply that result by \(-5\): \[ 25 \times (-5) = -125 \]

5. Substitute back into the expression: \[ (-5)^{-3} = \frac{1}{-125} = -\frac{1}{125} \]

Now, from the calculations, we find that \(x = -125\).

The response is:

• x = −125
• x is equal to negative 125