Question

1. (3pr²)²

Explanation:

Step1: Apply power of a product rule

The power of a product rule states that \((ab)^n = a^n b^n\). So for \((3pr^2)^2\), we can apply this rule to each factor inside the parentheses.
\((3pr^2)^2 = 3^2 \times p^2 \times (r^2)^2\)

Step2: Simplify each term

• Simplify \(3^2\): \(3^2 = 9\)
• For \((r^2)^2\), we use the power of a power rule \((a^m)^n = a^{m \times n}\). So \((r^2)^2 = r^{2\times2}=r^4\)
• The term \(p^2\) remains as it is.

Putting it all together, we have \(9\times p^2\times r^4 = 9p^2r^4\)

Answer:

\(9p^2r^4\)