To evaluate the expression [tex]\((-2)^5 + 4 \cdot (-15 + 9)(3) = 4\)[/tex], let's break it down step by step using the order of operations:
1. Evaluate expressions inside parentheses first:
The first parentheses we address is [tex]\((-15 + 9)\)[/tex].
[tex]\[
-15 + 9 = -6
\][/tex]
Now the expression becomes:
[tex]\[
(-2)^5 + 4 \cdot (-6)(3)
\][/tex]
2. Next, handle the exponents:
Evaluate [tex]\((-2)^5\)[/tex] as follows:
[tex]\[
(-2)^5 = -32
\][/tex]
Now the expression becomes:
[tex]\[
-32 + 4 \cdot (-6)(3)
\][/tex]
3. Perform multiplication from left to right:
There are two multiplication operations to perform: [tex]\(4 \cdot (-6)\)[/tex] and then the result multiplied by 3.
[tex]\[
4 \cdot (-6) = -24
\][/tex]
[tex]\[
-24 \cdot 3 = -72
\][/tex]
Now the expression becomes:
[tex]\[
-32 + (-72)
\][/tex]
4. Finally, perform the addition (or adding a negative number, which is essentially subtraction):
[tex]\[
-32 + (-72) = -104
\][/tex]
So, the value of the expression [tex]\((-2)^5 + 4 \cdot (-15 + 9)(3)\)[/tex] is [tex]\(-104\)[/tex]. However, it seems there's a mistake in aligning with the given information which states a different expected answer. According to the given answer, only evaluating [tex]\(-15 + 9\)[/tex] directly yields:
[tex]\[
-15 + 9 = -6
\][/tex]
