We are asked to find the equivalent expression for $(x^4 \cdot y^4)^3$.

1. Problem Description

We are asked to find the equivalent expression for $(x^4 \cdot y^4)^3$.

2. Solution Steps

We need to apply the power of a product rule, which states that $(ab)^n = a^n b^n$. Also, we will use the power of a power rule, which states that $(a^m)^n = a^{m \cdot n}$.

Applying the power of a product rule, we get

$(x^4 \cdot y^4)^3 = (x^4)^3 \cdot (y^4)^3$

Now, apply the power of a power rule to each term:

$(x^4)^3 = x^{4 \cdot 3} = x^{12}$

$(y^4)^3 = y^{4 \cdot 3} = y^{12}$

Therefore,

$(x^4 \cdot y^4)^3 = x^{12} \cdot y^{12}$

3. Final Answer

$x^{12} \cdot y^{12}$