Let's simplify the given expression:

The expression is: 

\[
2u^0 \cdot \left( 2u \right) \cdot \left( u - 8 \right)
\]

### Step 1: Simplify \(2u^0\)
Since \( u^0 = 1 \) for any \( u \) (except \( u = 0 \)), we have:

\[
2u^0 = 2 \times 1 = 2
\]

So, the expression becomes:

\[
2 \cdot (2u) \cdot (u - 8)
\]

### Step 2: Simplify the multiplication
Now, multiply \(2\) by \(2u\):

\[
2 \cdot 2u = 4u
\]

So the expression now is:

\[
4u \cdot (u - 8)
\]

### Step 3: Distribute \(4u\) across \( (u - 8) \)
\[
4u \cdot u - 4u \cdot 8
\]

This simplifies to:

\[
4u^2 - 32u
\]

### Final Answer:
\[
4u^2 - 32u
\]

This is the simplified form of the given expression.

Would you like further details or have any questions?

Here are some related questions you might be interested in:

1. What is the significance of the zero exponent rule?
2. How does distributing multiplication over subtraction work in algebra?
3. What happens when the exponent is negative instead of zero?
4. How would the expression change if there were more terms in the parentheses?
5. Can the expression \(4u^2 - 32u\) be factored further?

**Tip:** Always remember to simplify the exponents first before proceeding with other operations in an expression!

Learn how to simplify the algebraic expression 2u^0(2u)(u - 8) step by step using the zero exponent rule and the distributive property. This solution covers key algebraic concepts, suitable for students in Grades 6-8.

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