In the laws of exponents, what occurs when raising a power to a power?

When raising a power to a power in the laws of exponents, the exponents are multiplied. For instance, if we have ((a^m)^n), this expression means that the base (a) (which is being raised to the power (m)) is then raised to another power (n). According to the rule, this will simplify to (a^{m \times n}).

This rule is fundamental in exponentiation and helps to maintain consistency across mathematical calculations involving powers. When learning about exponents, it's crucial to remember that multiplying the exponents results from the repeated application of the base, which happens (m) times first and then (n) times thereafter.

The other choices do not correctly describe what happens when raising a power to a power. Adding exponents applies when multiplying like bases, merging base numbers is not a concept applicable in this context, and simplifying fractions relates to rational expressions rather than the operation of exponentiation. Understanding these rules is essential for further studies in mathematics, especially when dealing with algebraic expressions involving powers.