Question

Question was provided via image upload.

Explanation:

Step1: Apply power of a product rule

The power of a product rule states that \((ab)^n = a^n b^n\). For \((-2xy^2)^2\), we apply this rule to each factor: \((-2)^2 \cdot x^2 \cdot (y^2)^2\).

Step2: Simplify each term

• Simplify \((-2)^2\): \((-2)^2 = 4\).
• Simplify \((y^2)^2\) using the power of a power rule \((a^m)^n = a^{mn}\): \((y^2)^2 = y^{2\times2} = y^4\).
• The term \(x^2\) remains as is.

Now, multiply the simplified terms together: \(4 \cdot x^2 \cdot y^4 = 4x^2y^4\).

Answer:

\(4x^2y^4\)