Question

hat 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)
Responses

x=−125
x is equal to negative 125

x=15
x is equal to 15

x=125
x is equal to 125

x=−15

Answer 1

Let's go through the calculation step by step.

1. We start with the expression \((−5)^{-3}\). According to the negative exponent rule, this can be rewritten as:
\[
(−5)^{-3} = \frac{1}{(−5)^3}
\]

2. Next, we need to calculate \((−5)^3\):
\[
(−5)^3 = (−5) \times (−5) \times (−5)
\]

Calculating this step by step:
- First, calculate \((−5) \times (−5) = 25\).
- Then, multiply that result by \((−5)\):
\[
25 \times (−5) = -125
\]

3. Thus, we have:
\[
(−5)^3 = -125
\]

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

Now, we see that the expression \((−5)^{-3}\) evaluates to:
\[
(−5)^{-3} = -\frac{1}{125}
\]

However, if we're evaluating just \((−5)^3\) here for \(x\) in:
\[
(−5)^{-3}=1(−5)^{3}=1(−5)(−5)(−5)=1x
\]
we find that \(x = (−5)^3 = -125\).

So, the value of \(x\) is:
\[
\boxed{-125}
\]