Question

$(2x^{3})^{2}$

Explanation:

Step1: Apply power - of - a - product rule

According to the rule \((ab)^n=a^n\times b^n\), for \((2x^{3})^{2}\), we have \(2^{2}\times(x^{3})^{2}\).
\[2^{2}\times(x^{3})^{2}\]

Step2: Calculate \(2^{2}\) and apply power - of - a - power rule

First, \(2^{2}=4\). Second, according to the rule \((a^{m})^{n}=a^{mn}\), for \((x^{3})^{2}\), we have \(x^{3\times2}=x^{6}\). Then \(4\times x^{6}=4x^{6}\).
\[4x^{6}\]

Answer:

\(4x^{6}\)