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) = 1/x

What is the value of x?

Answer 1

To find the value of the expression \((-5)^{-3}\), we can follow the steps you've outlined and simplify correctly.

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

2. Expand the power:
\[
(-5)^3 = (-5) \times (-5) \times (-5) = 25 \times (-5) = -125
\]
Thus,
\[
(-5)^{-3} = \frac{1}{-125}
\]

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

Now, the last part of your original question asked for \(x\) in \(1/x\) where \(x = (-5)^3\). Since we found:
\[
x = (-5)^3 = -125
\]

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