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To simplify the expression \((y^5)^4 \cdot y^7\), you can use the power of a power rule and the product of powers rule from exponent rules.

1. Apply the power of a power rule: \((a^m)^n = a^{m \cdot n}\). Here, \((y^5)^4 = y^{5 \cdot 4} = y^{20}\).

2. Now your expression looks like this: \(y^{20} \cdot y^7\).

3. Use the product of powers rule: \(a^m \cdot a^n = a^{m+n}\). Thus, \(y^{20} \cdot y^7 = y^{20+7} = y^{27}\).

So, the simplified expression is:

\[ y^{27} \]