In the expression \((3^5)^2\), the base is \(3\) and the exponent is \(5 \times 2\).
You can simplify the expression using the property of exponents \((a^m)^n = a^{m \cdot n}\):
\[ (3^5)^2 = 3^{5 \cdot 2} = 3^{10} \]
So, the base is \(3\) and the exponent is \(10\).