Two students have bank accounts:
Sama: $ (4^(3)*4^(-4))/((4^(2))^(-5))
Jimena: $ (3*(3^(8))^(2))/((3^(2))^(3)*3^(0))
Which person has the most money in their account?
You cannot compare that total amount because the bases are different.
Sama
Jimena
They have the same amount of money
To determine who has the most money in their account, we need to simplify the expressions.
For Sama:
$ (4^(3)*4^(-4))/((4^(2))^(-5))
Using the rule of exponents, we can simplify this to:
$ (4^(3-4))/((4^(2*(-5))))
Which further simplifies to:
$ (4^(-1))/((4^(-10)))
Simplifying this, we have:
$ (1/4)/((1/4^10))
$ (1/4)/(1/4^10)
$ (1/4)/(1/1,048,576)
$ (1/4)/(1,048,576)
To divide by a fraction, we can multiply by its reciprocal. So:
$ (1/4)*(1,048,576/1)
$ 262,144/1
Therefore, Sama has $262,144 in her account.
For Jimena:
$ (3*(3^(8))^(2))/((3^(2))^(3)*3^(0))
Using the rules of exponents, we can simplify this to:
$ (3*(3^(16))/((3^(2))^(3)*1)
$ (3*(3^(16))/(3^(6))*1)
Using the rule of exponents to divide, we have:
$ (3^(16-6))/1
$ (3^10)/1
Therefore, Jimena has $59,049 in her account.
Comparing the amounts, Sama has $262,144 while Jimena has $59,049. Therefore, Sama has more money in her account.