Certainly! Let's go through the steps to evaluate the expression [tex]\(-2^3\)[/tex]:
1. Understand the expression: The given mathematical expression is [tex]\(-2^3\)[/tex].
- The "-" sign outside the base "2" indicates that we are dealing with a negative value.
- The exponent "^3" tells us we need to raise the base "2" to the power of 3.
2. Apply exponentiation first: According to the order of operations (often remembered by the acronym PEMDAS/BODMAS), we need to handle the exponentiation before applying the negative sign.
- Calculate [tex]\(2^3\)[/tex]. This means we multiply 2 by itself two more times:
[tex]\[
2 \times 2 \times 2 = 8
\][/tex]
3. Apply the negative sign: Now that we have the result of the exponentiation (which is 8), we need to apply the negative sign that was in front of the original expression.
- So, [tex]\(-2^3 = -(2^3) = -8\)[/tex].
Therefore, the value of [tex]\(-2^3\)[/tex] is [tex]\(-8\)[/tex].
