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Let's simplify Question 4:

The expression is:

\[
(2x^3)(4x)^2(-3x^4)^0
\]

### Step 1: Handle any zero exponents
\[
(-3x^4)^0 = 1
\]
Since any non-zero number raised to the power of zero is 1, this term simplifies to 1.

Now we are left with:
\[
(2x^3)(4x)^2
\]

### Step 2: Simplify \((4x)^2\)
\[
(4x)^2 = 4^2 \cdot x^2 = 16x^2
\]

### Step 3: Multiply the remaining terms
Now we multiply \(2x^3\) by \(16x^2\):
\[
2x^3 \cdot 16x^2 = (2 \cdot 16) \cdot (x^3 \cdot x^2) = 32x^{3+2} = 32x^5
\]

### Final Answer:
The simplified form is:
\[
32x^5
\]

Let me know if you'd like more details or explanations.

Here are 5 related questions:
1. How do you simplify expressions with negative exponents?
2. What happens when you raise a fraction to a negative power?
3. How do you handle fractional exponents in a similar expression?
4. Can you explain the properties of exponents with product and quotient rules?
5. How do you simplify an expression with both variables and constants raised to powers?

**Tip:** When multiplying terms with the same base, remember to add the exponents!

Learn how to simplify the expression (2x^3)(4x)^2(-3x^4)^0 step by step. This algebraic problem involves exponent rules such as the zero exponent rule and multiplication of exponential terms. Suitable for students in Grades 8-10.

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