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.
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
1 answer
1 answer