Let's break down and simplify the expression step by step:

The given expression is:

\[
4 \times (3^2 - 5 \times 2)^3
\]

### Step 1: Simplify inside the parentheses

First, evaluate \(3^2\) and \(5 \times 2\):

\[
3^2 = 9 \quad \text{and} \quad 5 \times 2 = 10
\]

So, the expression inside the parentheses becomes:

\[
9 - 10 = -1
\]

### Step 2: Cube the result

Now, cube \(-1\):

\[
(-1)^3 = -1
\]

### Step 3: Multiply by 4

Finally, multiply by 4:

\[
4 \times (-1) = -4
\]

Thus, the value of the expression is:

\[
\boxed{-4}
\]

Do you want more details, or have any questions?

Here are 5 related questions:
1. How would the answer change if the power was 4 instead of 3?
2. What happens if we change the base of the exponent to 4 instead of 3?
3. Can you apply this process to simplify \( 5 \times (2^3 - 4)^2 \)?
4. How does the value of the expression change if we modify the subtraction inside the parentheses?
5. What is the effect of changing the multiplication factor (e.g., from 4 to 6)?

**Tip**: When simplifying complex expressions, always follow the order of operations: parentheses first, then exponents, followed by multiplication/division, and addition/subtraction.

Explore how to simplify the expression 4*(3^2-5*2)^3 with a clear step-by-step guide. This problem involves core math concepts such as exponentiation and the order of operations, making it perfect for students in Grades 6-8. Learn how to evaluate powers, simplify expressions within parentheses, and apply multiplication.

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