Question

number 12
$(3x^3)^2$
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Explanation:

Step1: Apply power of a product rule

The power of a product rule states that \((ab)^n = a^n b^n\). For \((3x^3)^2\), we apply this rule: \(3^2 \times (x^3)^2\).

Step2: Simplify each term

First, simplify \(3^2 = 9\). Then, for \((x^3)^2\), use the power of a power rule \((a^m)^n = a^{mn}\), so \((x^3)^2 = x^{3\times2}=x^6\).

Step3: Multiply the results

Multiply the simplified terms: \(9\times x^6 = 9x^6\).

Answer:

\(9x^6\)