To determine the value of the expression [tex]\((-2)^5\)[/tex], we need to multiply [tex]\(-2\)[/tex] by itself five times. This involves repeated multiplication, as follows:
[tex]\[
(-2) \times (-2) \times (-2) \times (-2) \times (-2)
\][/tex]
Let’s proceed step-by-step with the multiplications:
1. First, multiply the first two terms:
[tex]\[
(-2) \times (-2) = 4
\][/tex]
This is because the product of two negative numbers is positive.
2. Next, multiply the result by the next [tex]\(-2\)[/tex]:
[tex]\[
4 \times (-2) = -8
\][/tex]
Multiplying a positive number by a negative number yields a negative result.
3. Continue by multiplying [tex]\(-8\)[/tex] by another [tex]\(-2\)[/tex]:
[tex]\[
-8 \times (-2) = 16
\][/tex]
Multiplying two negative numbers gives a positive result again.
4. Finally, multiply the result by the last [tex]\(-2\)[/tex]:
[tex]\[
16 \times (-2) = -32
\][/tex]
Therefore, the value of the expression [tex]\((-2)^5\)[/tex] is:
[tex]\[
\boxed{-32}
\][/tex]
