Question

question
simplify:
\\((4p^2)^3\\)

Explanation:

Step1: Apply power of a product rule

The power of a product rule states that \((ab)^n = a^n b^n\). So for \((4p^2)^3\), we can apply this rule as \(4^3\times(p^2)^3\).

Step2: Calculate \(4^3\) and \((p^2)^3\)

First, calculate \(4^3\): \(4^3 = 4\times4\times4 = 64\).
Then, use the power of a power rule \((a^m)^n = a^{m\times n}\) for \((p^2)^3\). Here, \(m = 2\) and \(n = 3\), so \((p^2)^3 = p^{2\times3}=p^6\).

Step3: Multiply the results

Multiply the two results from Step 2: \(64\times p^6 = 64p^6\).

Answer:

\(64p^6\)