Question

question
fully simplify.
\\((3xy^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 \((3xy^4)^4\), we can apply this rule to each factor inside the parentheses.
\((3xy^4)^4 = 3^4 \cdot x^4 \cdot (y^4)^4\)

Step2: Calculate the powers

First, calculate \(3^4\), which is \(3\times3\times3\times3 = 81\). Then, for the power of a power rule \((a^m)^n = a^{m\times n}\), so \((y^4)^4 = y^{4\times4}=y^{16}\). And \(x^4\) remains as it is.
Putting it all together, we have \(81x^4y^{16}\).

Answer:

\(81x^4y^{16}\)