Let's simplify the given expression step by step:

The expression is:

\[
-24y^4 + (2x^0y^2)^2
\]

### Step 1: Simplify the term \( 2x^0 \)
Since \( x^0 = 1 \), we can rewrite the term as:

\[
2x^0 = 2 \cdot 1 = 2
\]

Thus, the term \( (2x^0y^2)^2 \) becomes:

\[
(2y^2)^2
\]

### Step 2: Apply the power to the expression \( (2y^2)^2 \)
Now, square both the constant and the variable inside the parentheses:

\[
(2y^2)^2 = 2^2 \cdot (y^2)^2 = 4y^4
\]

### Step 3: Substitute the simplified term back into the expression
Now we can rewrite the original expression as:

\[
-24y^4 + 4y^4
\]

### Step 4: Combine like terms
Both terms involve \( y^4 \), so we can combine them:

\[
-24y^4 + 4y^4 = (-24 + 4)y^4 = -20y^4
\]

### Final Answer:
\[
-20y^4
\]

Would you like more details on any step, or do you have any questions?

Here are five related questions for practice:
1. Simplify \( -10y^3 + 5y^3 \).
2. Simplify \( (3x^2y)^3 \).
3. Simplify \( -15z^6 + 3z^6 \).
4. What is \( (4x^0z^5)^2 \)?
5. Simplify \( (x^2y^3)^2 \).

**Tip:** Always apply exponent rules carefully when simplifying expressions involving powers.

Explore the step-by-step simplification of the polynomial expression -24y^4 + (2x^0y^2)^2. This guide covers exponent rules, combining like terms, and simplifying polynomial expressions. Suitable for Grades 9-11 algebra students.

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