Let's solve it step-by-step:
1. The expression given is [tex]\((-2)^{-5}\)[/tex].
2. The negative exponent indicates that we need the reciprocal of the base raised to the positive exponent. Specifically:
[tex]\[
a^{-n} = \frac{1}{a^n}
\][/tex]
3. Applying this rule to our problem:
[tex]\[
(-2)^{-5} = \frac{1}{(-2)^5}
\][/tex]
4. Now we need to calculate [tex]\((-2)^5\)[/tex].
5. Remember, raising a negative number to an odd exponent results in a negative outcome. Therefore:
[tex]\[
(-2)^5 = -32
\][/tex]
6. Putting it all together, we get:
[tex]\[
(-2)^{-5} = \frac{1}{-32} = -0.03125
\][/tex]
So, the value of [tex]\((-2)^{-5}\)[/tex] is [tex]\(\boxed{-0.03125}\)[/tex].
