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fully simplify.
$(3x^{3}y^{5})^{4}$

Explanation:

Step1: Apply power - of - product rule

$$(ab)^n=a^n\cdot b^n$$
So, \((3x^{3}y^{5})^{4}=3^{4}\cdot(x^{3})^{4}\cdot(y^{5})^{4}\)

Step2: Calculate \(3^{4}\)

\(3^{4}=3\times3\times3\times3 = 81\)

Step3: Apply power - of - power rule \((a^{m})^{n}=a^{mn}\)

For \((x^{3})^{4}\), we have \(x^{3\times4}=x^{12}\)
For \((y^{5})^{4}\), we have \(y^{5\times4}=y^{20}\)

Answer:

\(81x^{12}y^{20}\)