Question

1. \\((4a^3)^2\\)

Explanation:

Step1: Apply power of a product rule

The power of a product rule states that \((xy)^n = x^n y^n\). So for \((4a^3)^2\), we apply this rule:
\((4a^3)^2 = 4^2 \times (a^3)^2\)

Step2: Simplify each term

First, calculate \(4^2\): \(4^2 = 16\)
Then, simplify \((a^3)^2\) using the power of a power rule \((x^m)^n = x^{m \times n}\). So \((a^3)^2 = a^{3 \times 2} = a^6\)
Now, multiply the two simplified terms together:
\(4^2 \times (a^3)^2 = 16 \times a^6 = 16a^6\)

Answer:

\(16a^6\)