Answer:
[tex]-\frac{1}{32}[/tex] or -0.03125
Skills needed: Exponents
Step-by-step explanation:
1) Negative exponent means 1 over if it was positive:
[tex]2^{-2} = \frac{1}{2^2}[/tex]
In this case: [tex]-2^{-5}=\frac{1}{(-2)^5}[/tex]
2) Let's expand the [tex](-2)^5[/tex] part:
Remember that the exponent (the smaller number in the top-right) shows how many times the base (bigger number) is multiplied by itself.
In this case:
[tex](-2)^5[/tex] = [tex]-2*-2*-2*-2*-2[/tex]
We know that: [tex]-2*-2=4[/tex]
So the above simplifies into: [tex]4 * 4 * -2[/tex] = [tex]16*-2[/tex] = [tex]-32[/tex]
3) That is the denominator in the fraction:
[tex]\frac{1}{-32}[/tex] which is [tex]-\frac{1}{32}[/tex]
