Let's simplify the expressions for Sama and Jimena.
For Sama: \[ Sama = \frac{4^3 \cdot 4^{-4}}{(4^2)^{-5}} \]
First, simplify the numerator: \[ 4^3 \cdot 4^{-4} = 4^{3 - 4} = 4^{-1} \]
Now simplify the denominator: \[ (4^2)^{-5} = 4^{-10} \]
Then the expression for Sama becomes: \[ Sama = \frac{4^{-1}}{4^{-10}} = 4^{-1 - (-10)} = 4^{9} \]
Now calculate \(4^9\): \[ 4^9 = (2^2)^9 = 2^{18} \]
For Jimena: \[ Jimena = \frac{3 \cdot (3^8)^2}{(3^2)^3 \cdot 3^0} \]
First, simplify the numerator: \[ (3^8)^2 = 3^{16} \implies 3 \cdot 3^{16} = 3^{1 + 16} = 3^{17} \]
Now simplify the denominator: \[ (3^2)^3 = 3^{6} \text{ and } 3^0 = 1 \implies 3^6 \cdot 3^0 = 3^{6} \]
Then the expression for Jimena becomes: \[ Jimena = \frac{3^{17}}{3^{6}} = 3^{17 - 6} = 3^{11} \]
Now, we need to compare \(4^9\) and \(3^{11}\).
Convert both to powers of 2, if possible: \[ 4^9 = (2^2)^9 = 2^{18} \] \[ 3^{11} = 3^{11} \text{ (cannot be expressed easily in base 2)} \]
Now, calculate approximate values: \[ 2^{18} = 262144 \] \[ 3^{11} = 177147 \]
So if we compare \(262144\) (for Sama) to \(177147\) (for Jimena), we find that: \[ 262144 > 177147 \]
Thus, Sama has the most money in her account.
The answer is: Sama.