What is (a^m)^n equal to?

The expression ((a^m)^n) can be simplified using the laws of exponents, specifically the power of a power property. This property states that when you raise a power to another power, you multiply the exponents.

In this case, you start with (a^m), which means (a) is raised to the power of (m). When this expression is raised to the power of (n), you multiply the exponent (m) by (n). Therefore, ((a^m)^n) becomes (a^{m \cdot n}), which is written as (a^{mn}).

This demonstrates why (a^{mn}) is the correct simplification of ((a^m)^n). The other options do not align with the laws of exponents, leading to incorrect simplifications or expressions that do not properly represent the relationship established by the original expression.