What happens to the exponent when raising a power to another power?

When raising a power to another power, the correct mathematical operation involves multiplying the exponents. This is based on the rule of exponents that states when you have a number in the form of ( (a^m)^n ), where ( a ) is the base, and ( m ) and ( n ) are the exponents, you can simplify it to ( a^{m \cdot n} ).

For example, if you take ( (2^3)^2 ), you can multiply the exponents: ( 3 \cdot 2 = 6 ). Thus, ( (2^3)^2 = 2^6 ). This rule helps simplify expressions involving exponents and is essential in many areas of mathematics, including algebra and calculus.

Other choices misinterpret how exponents should be handled in this context. Adding exponents applies in other rules of exponents, but not in this specific case. Squaring or ignoring the exponents does not align with the fundamental properties of exponents either, leading to incorrect conclusions if they were applied.