[ x = 5(-2)(-3)^4 - 3(-2)^2(-3)^3 + 7(-2)^3(-3)^2 + 5(-2)^5 ]

Let's break down the expression step by step:

Given:
\[
x = 5(-2)(-3)^4 - 3(-2)^2(-3)^3 + 7(-2)^3(-3)^2 + 5(-2)^5
\]

### Step 1: Evaluate each power and then multiply.

1. **First Term: \(5(-2)(-3)^4\)**  
   \[
   (-3)^4 = 81
   \]
   \[
   5(-2)(81) = 5 \times -2 \times 81 = -810
   \]

2. **Second Term: \(-3(-2)^2(-3)^3\)**  
   \[
   (-2)^2 = 4
   \]
   \[
   (-3)^3 = -27
   \]
   \[
   -3 \times 4 \times -27 = -3 \times -108 = 324
   \]

3. **Third Term: \(7(-2)^3(-3)^2\)**  
   \[
   (-2)^3 = -8
   \]
   \[
   (-3)^2 = 9
   \]
   \[
   7 \times -8 \times 9 = 7 \times -72 = -504
   \]

4. **Fourth Term: \(5(-2)^5\)**  
   \[
   (-2)^5 = -32
   \]
   \[
   5 \times -32 = -160
   \]

### Step 2: Combine all terms together:
\[
x = -810 + 324 - 504 - 160
\]
\[
x = -810 - 504 - 160 + 324
\]
\[
x = -1474 + 324 = -1150
\]

So, the final value of \( x \) is \(\boxed{-1150}\).

Would you like further details or have any questions?

---

Here are 5 related questions:
1. What is the value of \( (-3)^4 + (-2)^3 \)?
2. How do you evaluate powers of negative numbers?
3. What happens if we change the signs of coefficients in this expression?
4. Can you expand the expression using the distributive property?
5. What if \( x \) was a variable instead of a number? How would the evaluation change?

**Tip:** Always be cautious when working with negative bases and exponents, as their results depend heavily on whether the exponent is even or odd.

x = 5(-2)(-3)^4 - 3(-2)^2(-3)^3 + 7(-2)^3(-3)^2 + 5(-2)^5

Discover how to evaluate the algebraic expression 5(-2)(-3)^4 - 3(-2)^2(-3)^3 + 7(-2)^3(-3)^2 + 5(-2)^5 with a step-by-step solution. This problem covers key concepts like powers of negative numbers and the order of operations. Ideal for students in Grades 9-11.

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