Okay, let’s evaluate the expression [tex]\( (-2)^4 \)[/tex] step by step to understand why [tex]\( (-2)^4 \neq -8 \)[/tex].
1. Understanding the Expression:
- We need to evaluate the value of [tex]\((-2)^4\)[/tex].
- This means [tex]\((-2)\)[/tex] multiplied by itself four times.
2. Step-by-Step Multiplication:
- First, calculate [tex]\((-2) * (-2)\)[/tex]:
[tex]\[
(-2) * (-2) = 4
\][/tex]
Multiplying two negative numbers results in a positive number.
- Next, calculate [tex]\(4 * (-2)\)[/tex]:
[tex]\[
4 * (-2) = -8
\][/tex]
Multiplying a positive number by a negative number results in a negative number.
- Finally, calculate [tex]\((-8) * (-2)\)[/tex]:
[tex]\[
(-8) * (-2) = 16
\][/tex]
Multiplying two negative numbers results in a positive number.
3. Conclusion:
- After performing the above series of multiplications, we find that:
[tex]\[
(-2)^4 = 16
\][/tex]
Therefore, the correct evaluation of [tex]\( (-2)^4 \)[/tex] is 16, not -8.
