Question

1. $(3k^4)^4$

Explanation:

Step1: Apply power of a product rule

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

Step2: Calculate \(3^4\) and \((k^4)^4\)

First, \(3^4 = 3\times3\times3\times3 = 81\). Then, using the power of a power rule \((a^m)^n = a^{m\times n}\), for \((k^4)^4\), we have \(k^{4\times4}=k^{16}\).

Step3: Multiply the results

Multiply the two results together: \(81\times k^{16}=81k^{16}\).

Answer:

\(81k^{16}\)