The expression provided is $(y^{13})^4$. To simplify this, we apply the power of a power rule in exponents, which states:

$(a^m)^n = a^{m \cdot n}$

Applying this rule to $(y^{13})^4$:

$(y^{13})^4 = y^{13 \cdot 4} = y^{52}$

Thus, $(y^{13})^4 = y^{52}$.

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Related Questions:

1. How do you simplify $(x^5)^6$?
2. What is the general rule for multiplying exponents when bases are the same?
3. How do you handle negative exponents in expressions?
4. What happens if you raise a number to the power of zero, like $x^0$?
5. How do you simplify $(2^3)^4$?

Tip: When dealing with exponents, always check if you can apply rules like power of a power, product of powers, or quotient of powers to simplify the expression.