Final answer:
The question involves applying rational exponents to simplify the fraction (e^m)^(1/2m). Upon simplification using the power multiplication rule, e^(m*(1/2m)) becomes e^(1/2), which is the square root of e. Since the same expression is in the numerator and denominator, the fraction simplifies to 1.
Step-by-step explanation:
We are asked to apply the rational exponent to the numerator and the denominator of the fraction c = (e^m)^(1/2m). Firstly, we can use the rule of powers that states when raising a power to another power, you can multiply the exponents. In this case, we have e raised to the power of m, and this whole term is then raised to the power of 1/2m.
Mathematically, we can write this as e^(m*(1/2m)). Since m and 1/2m are multiples, they can effectively cancel each other out, leaving us with e^(1/2), which is the square root of e.
Looking at our initial expression, we see that the numerator and the denominator are the same, therefore, regardless of the simplification we performed, the fraction reduces to 1. This is because any number or expression divided by itself equals 1, following the properties of division of exponentials, squaring of exponentials, and taking square roots of exponentials.