To evaluate the expression [tex]\( -2^3 \)[/tex], follow these steps:
1. Identify the base and exponent: Here, the base is [tex]\(-2\)[/tex] and the exponent is [tex]\(3\)[/tex]. This means we are raising [tex]\(-2\)[/tex] to the power of [tex]\(3\)[/tex].
2. Understand the exponentiation: Raising a number to a power means multiplying the number by itself as many times as the exponent indicates. In this case, we need to multiply [tex]\(-2\)[/tex] by itself three times.
3. Perform the multiplication:
[tex]\[
(-2)^3 = (-2) \times (-2) \times (-2)
\][/tex]
4. Calculate step-by-step:
- First, multiply the first two [tex]\(-2\)[/tex]'s:
[tex]\[
(-2) \times (-2) = 4
\][/tex]
- Next, multiply the result by the remaining [tex]\(-2\)[/tex]:
[tex]\[
4 \times (-2) = -8
\][/tex]
5. Combine the result: After performing the multiplications, we get:
[tex]\[
(-2)^3 = -8
\][/tex]
Therefore, the value of [tex]\( -2^3 \)[/tex] is [tex]\(-8\)[/tex].
