What is the result when you multiply the exponents of a power of a power?

When dealing with the powers of a power, the rule states that you multiply the exponents. This is a fundamental property of exponents, which can be summarized mathematically as follows:

If you have an expression of the form ((a^m)^n), where (a) is the base and (m) and (n) are the exponents, the operation of raising a power to another power requires you to multiply the exponents together. Therefore, the expression simplifies to (a^{(m \cdot n)}).

For instance, if you take ( (x^2)^3 ), applying the rule gives you ( x^{2 \cdot 3} = x^6).

This illustrates why multiplying the exponents is the correct operation when raising a power to another power, leading to the conclusion that when the base is the same, the correct procedure is to multiply the exponents together, aligning with the actual properties of exponents.