Question

simplify the expression ((n^{3}p)^{4}). write the variables in alphabetical order.

Explanation:

Step1: Apply the power of a product rule

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

Step2: Apply the power of a power rule

The power of a power rule states that \((a^m)^n = a^{m\cdot n}\). Applying this to \((n^{3})^{4}\):
\((n^{3})^{4}=n^{3\times4}=n^{12}\)

Step3: Combine the results

Combining the results from Step 1 and Step 2, we get:
\((n^{3}p)^{4}=n^{12}p^{4}\)

Answer:

\(n^{12}p^{4}\)